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Travelling Fires for
Structural Design
Jamie Stern-Gottfried
A thesis submitted for the degree of
Doctor of Philosophy
The University of Edinburgh
2011
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To my wife, Ina
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Abstract
Traditional methods for specifying thermal inputs for the structural fire analysis of
buildings assume uniform burning and homogeneous temperature conditions
throughout a compartment, regardless of its size. This is in contrast to the
observation that accidental fires in large, open-plan compartments tend to travel
across floor plates, burning over a limited area at any one time.
This thesis reviews the assumptions inherent in the traditional methods and
addresses their limitations by proposing a methodology that considers travelling
fires for structural design. Central to this work is the need for strong collaboration
between fire safety engineers to define the fire environment and structural fire
engineers to assess the subsequent structural behaviour.
The traditional hypothesis of homogeneous temperature conditions in post-
flashover fires is reviewed by analysis of existing experimental data from well-
instrumented fire tests. It is found that this assumption does not hold well and that
a rational statistical approach to fire behaviour could be used instead.
The methodology developed in this thesis utilises travelling fires to produce more
realistic fire scenarios in large, open-plan compartments than the conventional
methods that assume uniform burning and homogeneous gas phase temperatures
which are only applicable to small compartments. The methodology considers a
family of travelling fires that includes the full range of physically possible fire sizes
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within a given compartment. The thermal environment is split into two regions: the
near field (flames) and the far field (smoke away from the flames). Smaller fires
travel across a floor plate for long periods of time with relatively cool far field
temperatures, while larger fires have hotter far field temperatures but burn for
shorter durations.
The methodology is applied to case studies showing the impact of travelling fires on
generic concrete and steel structures. It is found that travelling fires have a
considerable impact on the performance of these structures and that conventional
design approaches cannot automatically be assumed to be conservative. The results
indicate that medium sized fires between 10% and 25% of the floor area are the most
onerous for a structure. Detailed sensitivity analyses are presented, showing that the
structural design and fuel load have a larger impact on structural behaviour than
any numerical or physical parameter required for the methodology.
This thesis represents a foundation for using travelling fires for structural analysis
and design. The impact of travelling fires is critical for understanding true structural
response to fire in modern, open-plan buildings. It is recommended that travelling
fires be considered more widely for structural design and the structural mechanics
associated with them be studied in more detail. The methodology presented in this
thesis provides a key framework for collaboration between fire safety engineers and
structural fire engineers to achieve these aims.
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Declaration
This thesis and the work described within have been completed solely by Jamie
Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis
Torero. Where others have contributed or other sources are quoted, full references
are given. This work has not been submitted for any other degree or professional
qualification.
Jamie Stern-Gottfried
2011
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Acknowledgements
Firstly I would like to thank my supervisor, friend, confidant, and certain future
collaborator Guillermo Rein for his constant encouragement, insightful guidance,
and contagious optimism. Our meetings in your office, telephone calls, emails, and
discussions wherever we happened to be were always welcomed and extremely
important for the development of this thesis. I am also grateful for the warm
hospitality you and Cecile have extended to me.
I would also like to thank my second supervisor José Luis Torero for providing
ideas and conversations that helped shape this work. Thank you for developing and
fostering a fantastic research group. It has been a genuine pleasure to be a part of it.
I am extremely grateful for the support of Arup in funding this research and
affording me time away from the office. In particular, thank you to Barbara Lane for
making this all happen and sticking by me through uncertain times. I am thankful
for all the support from my many colleagues past and present who gave their
thoughts on my work and covered for me when I was away, especially Paul,
Gabriele, and Hay Sun. I look forward to applying this work to our projects!
Additional thanks goes to all of the structural fire engineers at Arup and Edinburgh
who helped shed light on the previously dark subject to me of structural
engineering. Specifically, thanks to Graeme, Linus, Darlene, Charlotte, Hélène,
Allan, Sue, Neal, Alex, Susan, and Luke.
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Extra special thanks goes to Angus for not just listening to my thoughts, but
wanting to do something about them! Our collaboration has been extremely
rewarding and fun. I’m pleased that we can keep it up.
Thanks to all of the students and other friendly faces in the fire group at Edinburgh
for some great times and always making me feel welcome. Thanks to Wolfram and
Agustin for the wonderfully geeky fire dynamics conversations. And thanks to
Rorbo for graciously sharing his time with “The Boss” with me when I was in
Edinburgh and helping me navigate the Uni bureaucracy when I was not.
I am very grateful to all my family back in the USA for all you have done for me and
giving me such incredible support from a distance – thank you!
Lastly, and most importantly, thank you Ina. You have been an absolutely
incredible girlfriend, fiancée, and wife throughout this process. You have done so
much for me in terms of all the little things (the Sunday lunch breaks were always
delicious!), but also the big ones. For that I am extremely grateful and incredibly
happy to have you in my life.
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Contents
Abstract ................................................................................................................................. iii
Declaration ............................................................................................................................ v
Acknowledgements ........................................................................................................... vii
Contents ................................................................................................................................ ix
Scholarly Output ............................................................................................................... xiii
Preface ................................................................................................................................ xvii
1 Introduction ......................................................................................................................1
1.1 Traditional Methods ............................................................................................2
1.2 Non-Uniform Burning .........................................................................................4
1.3 Travelling Fires .....................................................................................................5
1.4 A New Methodology ...........................................................................................7
1.5 Collaboration ........................................................................................................8
2 Experimental Review of the Homogeneous Temperature
Assumption in Post-Flashover Compartment Fires ................................................11
2.1 Introduction ........................................................................................................11
2.2 The Homogeneous Temperature Assumption ..............................................12
2.2.1 Origins of the Assumption ................................................................12
2.2.2 Critiques of the Assumption .............................................................14
2.3 Experimental Review ........................................................................................15
2.3.1 Non-Uniform Burning in Experiments ............................................15
2.3.2 Travelling Fires ...................................................................................16
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2.3.3 Fire Tests with High Spatial Resolution ......................................... 17
2.3.4 Data Distributions .............................................................................. 25
2.3.5 Standard Deviation vs. Temperature Rise ...................................... 26
2.4 Effect of Temperature Heterogeneity on the Structure ................................ 30
2.5 Conclusions ........................................................................................................ 38
3 A Review of Travelling Fires in Structural Analysis ............................................ 43
3.1 Introduction ........................................................................................................ 43
3.2 Traditional Design Methods ............................................................................ 44
3.3 Limitations of the Uniform Burning Assumption ........................................ 46
3.3.1 Evidence from Experiments ............................................................. 48
3.3.2 Evidence from Accidental Fires ....................................................... 50
3.4 Pioneering Methods .......................................................................................... 51
3.4.1 Large Firecell Method - HERA New Zealand ................................ 51
3.4.2 Travelling Fires Methodology – University of Edinburgh ........... 54
3.5 Structural Response........................................................................................... 62
3.5.1 Steel Frame .......................................................................................... 63
3.5.2 Concrete Frame .................................................................................. 65
3.5.3 Vertically Travelling Fires ................................................................. 67
3.6 Practical Applications ....................................................................................... 69
3.7 Conclusions ........................................................................................................ 73
4 The Influence of Travelling Fires on a Concrete Frame ........................................ 81
4.1 Introduction ........................................................................................................ 81
4.2 Limitations of Current Design Fires ............................................................... 83
4.3 Travelling Fires .................................................................................................. 85
4.3.1 Temperature Definition ..................................................................... 85
4.3.2 Fire Size ............................................................................................... 87
4.4 Structural Failure Criteria ................................................................................ 88
4.5 Structural Modelling ......................................................................................... 89
4.5.1 Structural Arrangement .................................................................... 89
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4.6 Base Case Fires ...................................................................................................91
4.6.1 Structural and Thermal Analysis .....................................................93
4.7 Parametric Study ................................................................................................98
4.7.1 Far Field Definition ............................................................................98
4.7.2 Fire Shape and Path ..........................................................................101
4.8 Summary and Concluding Remarks .............................................................103
5 Refinement and Application of the Travelling Fires Methodology ..................109
5.1 Introduction ......................................................................................................109
5.2 Travelling Fires Framework ...........................................................................111
5.3 Analytical Model ..............................................................................................114
5.3.1 Burning Times ...................................................................................114
5.3.2 Near Field vs. Far Field ....................................................................116
5.3.3 Spatial Discretisation ........................................................................120
5.4 Application to a Generic Structure ................................................................124
5.5 Parameter Sensitivity Study ...........................................................................127
5.5.1 Fire Size ..............................................................................................127
5.5.2 Grid Size .............................................................................................130
5.5.3 Rebar Depth .......................................................................................133
5.5.4 Bay Location and Bay Size...............................................................135
5.5.5 Fuel Load Density and Heat Release Rate per Unit Area ...........138
5.5.6 Heat Transfer .....................................................................................139
5.5.7 Near Field Temperature ..................................................................141
5.5.8 Steel Structure ...................................................................................142
5.6 Comparison to Conventional Methods .........................................................146
5.7 Final Remarks ...................................................................................................147
6 Conclusions and Future Work ...................................................................................153
6.1 Conclusions .......................................................................................................153
6.2 Future Work ......................................................................................................155
6.2.1 Fire Environment ..............................................................................156
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6.2.2 Fire – Structure Interface ................................................................. 157
6.2.3 Structural Response ......................................................................... 158
Appendix A Heat Transfer Calculations ..................................................................... 163
A.1 Concrete Beam Temperatures ........................................................................ 163
A.2 Unprotected Steel Beam Temperatures ........................................................ 165
A.3 Protected Steel Beam Temperatures ............................................................. 166
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Scholarly Output
Journal Papers
Stern-Gottfried, J., Rein, G., Bisby, L.A., and Torero, J.L., “Experimental review
of the homogeneous temperature assumption in post-flashover compartment
fires”. Fire Safety Journal, Vol. 45, 2010, pp. 249-261.
Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling
fires on a concrete frame”. Engineering Structures, Vol. 33, 2011, pp. 1635-1642.
Invited Talks
“Fires in Large Compartments”, Invited Talk at The Rasbash Lecture, hosted by
The Institution of Fire Engineers, Andover, UK, 2008.
“Design Fires for Structural Analysis”, as part of the workshop on Structural
Fire Engineering prior to The 9th International Symposium on Fire Safety Science in
Karlsruhe, Germany, 2008.
Conference and Magazine Papers
Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "An Innovative Approach
to Design Fires for Structural Analysis of Non-Conventional Buildings: A Case
Study". International Workshop in Applications of Structural Fire Engineering,
Prague, Czech Republic, 2009.
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Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "A Novel Methodology for
Determining Design Fires for Structural Fire Analysis". 6th Mediterranean
Combustion Symposium, Corsica, France, 2009.
Stern-Gottfried, J., Rein, G., and Torero, J.L., "An Experimental Review of the
Homogeneous Temperature Assumption in Post-Flashover Compartment
Fires”. International Congress on Fire Protection and Life Safety in Buildings and
Transportation Systems, Santander, Spain, 2009.
Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel guide”, Fire Risk
Management, November 2009, pp. 12-16.
Stern-Gottfried, J., Rein, G., and Torero, J.L., "A Performance Based
Methodology Using Travelling Fires for Structural Analysis". 8th International
Conference on Performance-Based Codes and Fire Safety Design Methods, Lund
University, Sweden, June 2010.
Stern-Gottfried, J., Rein, G., and Torero, J.L., "Experimental Review of the
Homogeneous Temperature Assumption in Post-Flashover Compartment
Fires”. The 12th International Interflam Conference, University of Nottingham, UK,
July 2010.
Jonsdottir, A., Rein, G., and Stern-Gottfried, J., “Comparison of Resultant Steel
Temperatures Using Travelling Fires and Traditional Methods: A Case Study of
the Informatics Forum Building”. The 12th International Interflam Conference,
University of Nottingham, UK, July 2010.
Rein, G. and Stern-Gottfried, J., “Travelling Fires in Large Compartments:
Realistic fire dynamics for structural design”, International Conference on
Applications of Structural Fire Engineering, Prague, Czech Republic, Prague,
Czech Republic, 2011.
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Posters
Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "Design Fires for
Structural Analysis of Complex Buildings". The 9th International Symposium on
Fire Safety Science, Karlsruhe, Germany, 2008.
Stern-Gottfried, J., Rein, G., and Torero, J.L., "Experimental Review of the
Homogeneous Temperature Assumption in Post-Flashover Compartment
Fires". Spring Meeting of the British Section of the Combustion Institute, Edinburgh,
UK, 2010. (Awarded Best Poster).
Awards
David B. Gratz Scholarhip, 2010. Awarded by the Fire Safety Educational
Memorial Fund of the National Fire Protection Association (NFPA) in the USA
to a graduate student in Fire Science located outside the USA and Canada who
demonstrates scholarship achievement, leadership qualities, concern for
others/volunteerism, and contributions to international/national fire safety
activities.
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Preface
This thesis is written in manuscript format. As such each chapter is a standalone
document suitable for journal publication. The material is presented as follows:
Chapter 1 is a brief introduction to the concept of travelling fires and the
research presented in this thesis. While not a full manuscript, it is loosely based
on:
Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel Guide”, Fire Risk
Management, November 2009. pp. 12-16.
Chapter 2 presents a review of the homogeneous temperature assumption in
post-flashover fires that is invoked in many compartment fire models. This
manuscript has been published as:
Stern-Gottfried, J., Rein, G., Bisby, L.A., and Torero, J.L., “Experimental
review of the homogeneous temperature assumption in post-flashover
compartment fires”. Fire Safety Journal, Vol. 45, 2010, pp. 249-261.
Chapter 3 is a literature review of research in travelling fires for structural
analysis. This manuscript has been submitted for journal publication.
Chapter 4 presents a collaborative research effort with structural fire engineers.
The chapter investigates the impact of the travelling fires methodology
xviii
developed in this thesis on a generic concrete frame. In this work, I quantified
and reported on the thermal environment. The lead author performed and
reported on the structural analysis as part of his PhD thesis. This manuscript
has been published as:
Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of
travelling fires on a concrete frame”, Engineering Structures, Vol. 33, 2011,
pp. 1635-1642.
Chapter 5 presents the detailed development of the travelling fires
methodology with application to heating of a generic concrete structure. This
manuscript has been submitted for journal publication.
Chapter 6 is a conclusion for this thesis and presents recommended future
work. This chapter is not intended to be a published manuscript.
Appendix A provides details of the heat transfer calculations utilised in
Chapters 2 and 5.
1
1 Introduction
Close inspection of accidental fires in large, open-plan compartments reveals that
they do not burn simultaneously throughout the entire enclosure. Instead, these
fires tend to move across floor plates as flames spread, burning over a limited area
at any one time. These fires have been labelled “travelling fires”.
Despite these observations, fire scenarios currently used for the structural fire
design of modern buildings are based on traditional methods that come from the
extrapolation of existing fire test data. Most of these data stem from tests performed
in small compartments that are almost cubic in nature. This test geometry allows for
good mixing of the fire gases and thus for a relatively uniform temperature
distribution throughout the compartment. While this behaviour is different from
that observed in real fires, it has generally been deemed a conservative, and
therefore appropriate, approach for structural fire design in the absence of better
and more relevant data. This approach might be considered acceptable for most
2
design cases, but the need for better optimisation of structural behaviour in fire will
eventually require a more realistic definition of the fire.
Computational methods for determining structural behaviour have matured over
the last decade and have enabled analysis of more complex structural systems. This
has led to an understanding that many modern structures do not behave in the same
manner as simpler, more traditional frame based systems. In order to address these
differences, and continue to enable innovation in structural design, a more
sophisticated characterisation of fire scenarios is required.
This thesis reviews the assumptions inherent in the traditional methods and
addresses their limitations by proposing a methodology to consider travelling fires
for structural design. Central to this work is the need for strong collaboration
between fire safety engineers to define the fire environment and structural fire
engineers to assess the subsequent structural behaviour.
1.1 Traditional Methods
It is important to understand the context of the current design methods to establish
a new methodology for design fires for structural analysis. Traditionally, structural
fire analysis has been based on one of two methods for characterising the fire
environment:
• The standard temperature-time curve (as specified by various standards,
such as BS 476 [1], ISO 834 [2], and ASTM E119 [3])
• Parametric temperature-time curves (such as that specified in Eurocode 1
[4]).
While both of these methods have great merits and represented breakthroughs in
the discipline at their times of adoption, it is recognised that they have limitations.
3
The standard temperature-time curve, which is used as the basis for the fire rating
system in most building codes and standards worldwide, was first published in
1917 [5]. The curve came from collating various fire tests into one idealised curve.
The tests that fed into the development of the standard fire were intended to
represent worst case fires in enclosures so that the structure could withstand
burnout. However, these tests were conducted and the standard fire created prior to
much scientific understanding of fire dynamics. Thus the standard fire, unlike a real
fire, has a relatively slow growth period, never reduces in temperature due to fire
decay, and is independent of building characteristics such as geometry, ventilation
and fuel load.
The next major landmark for structural fire analysis, in terms of design, was a
guidance document produced in Sweden in 1976 [6]. This work incorporated the
current understanding of compartment fire dynamics based on tests conducted in
small scale enclosures. The document presented the key factors of compartment fire
temperatures as the fuel load, ventilation, and the thermal properties of the wall
linings. The guide gave design recommendations and a series of temperature-time
curves for a wide range of the critical parameters, accounting for the cooling period
of the fire.
The Eurocode parametric temperature-time curve is based on the same fire science
as the Swedish design guide. The Eurocode parametric temperature-time curve was
developed to collapse all of the curves given in the Swedish guidance document
into a simplified mathematical form.
Eurocode 1 [4] states that the design equations for the parametric temperature-time
curve specified are only valid for compartments with floor areas up to 500m2 and
heights up to 4m. In addition the enclosure must have no openings through the
ceiling and the thermal properties of the compartment linings must be within a
limited range. As a result, common features in modern construction like large
4
enclosures, high ceilings, atria, large open spaces, multiple floors connected by
voids, and glass façades are excluded from its range of applicability. These
limitations, which are largely associated with the physical size and geometric
features of the experimental compartments on which the methods are based, ought
to be carefully considered when the method is applied to an engineering design
beyond the recommended ranges of applicability. This is particularly relevant given
the large floor plates and complicated architecture of modern buildings.
It is noted that the background document to the UK National Annex of Eurocode 1
[7] suggests that designers can ignore the given limitations on floor area and
compartment height and can expand the range of the compartment lining values.
While this allows engineers to use the equations on more practical applications, it
does not appear to address the observed travelling nature of real fires in large
compartments.
1.2 Non-Uniform Burning
The traditional methods mentioned above for specifying design fires for structural
engineering analysis assume spatially homogeneous temperature conditions. The
accuracy and range of validity of this assumption is examined in Chapter 2, using
the previously conducted fire tests of Cardington (1999) and Dalmarnock (2006).
Statistical analyses of the test measurements provide insights into the temperature
fields in the compartments. The temperature distributions are statistically examined
in terms of dispersion from the spatial compartment average. The results clearly
show that uniform temperature conditions are not present and variations from the
compartment averages exist. Peak local temperatures range from 23% to 75% higher
than the compartment average, with a mean peak increase of 38%. Local minimum
temperatures range from 29% to 88% below the spatial average, with a mean local
minimum temperature of 49%. The experimental data are then applied to typical
structural elements as a case study to examine the potential impact of the gas
5
temperature dispersion above the compartment average on element heating.
Compared to calculations using the compartment average, this analysis results in
increased element temperature rises of up to 25% and reductions of the time to
attain a pre-defined critical temperature of up to 31% for the 80th percentile
temperature increase. The results show that the homogeneous temperature
assumption does not hold well in post-flashover compartment fires. Instead, a
rational statistical approach to fire behaviour could be used in fire safety and
structural engineering applications.
This heterogeneity of the temperature field will be more pronounced when the
burning itself is not uniform, as is the case in travelling fires. A travelling fire is
when only a portion of a floor plate is fully involved in flames that then move to
other areas of the floor as burnout occurs in locations of earlier burning. The fire
travels as flames spread to unburnt fuel, partitions or false ceilings break and
ventilation changes through glazing failure.
Many large, accidental fires, such as those in the World Trade Center Towers 1, 2 [8]
and 7 [9] in New York in 2001, the Windsor Tower in Madrid, Spain in 2005 [10] and
the Faculty of Architecture building at TU Delft in the Netherlands in 2008 [11] were
all observed to travel across floor plates, and vertically between floors, rather than
burn uniformly for their duration. Similar observations were made of the Interstate
Bank fire in Los Angeles in 1988 [12] and the One Meridian Plaza fire in
Philadelphia in 1991 [13]. Travelling fires have also been observed experimentally in
compartments with non-uniform ventilation [14, 15, 16].
1.3 Travelling Fires
Based on the above, it can be seen that the concept of travelling fires is in direct
contrast to the fundamental nature of current design methods that assume uniform
conditions throughout a compartment for the entire duration of burning of a fire.
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A fire that burns uniformly within a large enclosure would generate high
temperatures, but only for a relatively short duration. However, a fire that travels
will still create elevated temperatures away from the fire (the far field) as well as
flame temperatures in the near field. A travelling fire can therefore inflict the
structure with elevated temperatures for longer durations. A travelling fire is
illustrated in Figure 1.1, showing the difference between the near field and far field.
Figure 1.1: Illustration of a travelling fire.
Due to the discrepancy between fire behaviour in actual incidents and that assumed
in traditional design methods, it is possible that current practices for structural
design do not consider a potentially worst case fire scenario. Non-uniform heating
across a compartment floor could cause a failure mechanism in the structure which
may not occur if uniform temperatures were applied to the structure. For example, a
cool, unheated bay in a multi-bay structure could produce high axial restraint forces
and that could result in failure of a heated element. In other situations, however,
traditional design methods may be overly conservative compared to the impact of a
real fire.
Far field (Tff) Near field (Tnf)
Near field
travels over
time
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1.4 A New Methodology
To address the limitations of the traditional methods, and provide the necessary
tools to enable a more realistic determination of a building’s response to fire, a
methodology has been developed that can incorporate the actual dynamics of a
travelling fire into structural analysis. This methodology will better enable
structural and architectural design innovation.
Chapter 3 is a literature review of travelling fire research. A brief background to the
traditional methods that assume uniform fires is given along with critiques of that
assumption, such as the heterogeneity of compartment temperatures and the
observation of travelling fires in both accidental events and controlled tests. The
research in travelling fires is reviewed, highlighting the pioneering work in the field
to date. The main challenge in developing tools for incorporating travelling fires
into design is the lack of large scale test data. Nonetheless, significant progress in
the field has been made and a robust methodology using travelling fires to
characterise the thermal environment for structural analysis has been developed.
The research in quantifying the structural response to travelling fires is also
reviewed.
Chapter 4 presents a collaborative analysis between fire engineers and structural fire
engineers. A basic version of the travelling fires methodology, using a family of
fires, is applied to a framed concrete structure. A Finite Element Model of the
generic concrete structure is used to study the impact of the family of fires; both
relative to one another and in comparison to the conventional methods. It is found
that travelling fires have a significant impact on the performance of the structure
and that the current design approaches cannot be assumed to be conservative.
Further, it is found that a travelling fire of approximately 25% of the floor plate in
size is the most severe in terms of structural response. It is concluded that the
8
travelling fires methodology is simple to implement, provides more realistic fire
scenarios, and is more conservative than current design methods.
Chapter 5 gives a more developed version of the methodology. Many of the
assumptions of the method are explored, and a robust spatial discretisation scheme
is adopted to characterise the far field variation of a linearly travelling fire. Heating
of a similar concrete structure to that used in Chapter 4 is examined. A detailed
sensitivity study is also conducted, highlighting the critical parameters for design. It
is found that the most sensitive parameters are related to the building design and its
use and not the physical assumptions or numerical implementation of the model.
1.5 Collaboration
As the disciplines of fire science and structural engineering are very disparate in
their knowledge base, but have a strong overlap in their application to structural
fire analysis, a high degree of collaboration between these disciplines is required
[17]. The travelling fires methodology developed and presented in this thesis has
been formulated with precisely this degree of multidisciplinary cooperation in
mind.
References
1 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:
Method for Determination of the Fire Resistance of Elements of Construction:
BSI, 1987.
2 ISO 834-1. Fire-resistance tests — Elements of building construction — Part 1:
General requirements
3 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings
Construction and Materials, 2000.
9
4 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on
structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.
5 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance
testing – Part II.” Fire Technology, Vol. 14, 1978, pp. 304-316.
6 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel
Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,
1976.
7 PD 6688-1-2:2007 Background paper to the UK National Annex to BS EN 1991-
1-2
8 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,
Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the
World Trade Center Towers. NIST NCSTAR 1-5, 2005.
9 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,
Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire
Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST
NCSTAR 1-9, 2008.
10 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based
analysis of a concrete building subjected to fire,” Advanced Research Workshop on
Fire Computer Modelling, Santander, Spain, 2007,
http://www.era.lib.ed.ac.uk/handle/1842/1988.
11 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT
Instituut voor Veilingheids – en Crisismanagement, 2008.
12 Routley, J.G., “Interstate Bank Building Fire, Los Angeles, California”, U.S. Fire
Administration Technical Report 022.
13 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One
Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration
Technical Report 049.
10
14 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation
Openings – Comparison of Long and Wide Enclosures”, The 6th International
Symposium on Fire Safety Science, Poitiers, France, 1999.
15 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,
“Natural Fires in Large Scale Compartments”, British Steel, 1994.
16 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of
the homogeneous temperature assumption in post-flashover compartment
fires”. Fire Safety Journal, 45, 2010, pp. 249-261.
17 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires.”
The 9th International Symposium on Fire Safety Science, Karlsruhe, Germany, 2008.
11
2 Experimental Review of
the Homogeneous Temperature
Assumption in Post-Flashover
Compartment Fires
2.1 Introduction
Post-flashover compartment fires are of particular relevance to the analysis of
structural fire performance because of their high severity. Traditional methods for
quantifying and modelling post-flashover fires for structural engineering analysis
assume homogeneous temperature conditions, i.e. the gas phase temperature
distribution is taken to be spatially uniform and does not have considerable
gradients. For example, the methodologies for structural fire analysis that use the
standard and parametric temperature-time curves assume this uniform temperature
12
regardless of the compartment size or fire power. This assumption has been
necessary to develop simple analytical solutions to the temperature evolution and
further the understanding of post-flashover compartment fires and subsequent
structural responses [1].
However, the accuracy and range of validity of the homogeneous temperature
assumption has not been thoroughly examined before. This is generally due to the
limited number of post-flashover fire experiments available and especially to the
low spatial resolution of temperature measurements used in such tests.
This paper reviews the validity of this assumption using previously conducted fire
tests. The tests chosen for these analyses are the Cardington (1999) and Dalmarnock
(2006) tests. The choices are based on the detailed instrumentation and the large
geometry of the tests. The paper also examines the impact of the departure from the
homogeneous temperature assumption on typical thermal analyses that represent
the basis behind structural fire calculations.
2.2 The Homogeneous Temperature Assumption
2.2.1 Origins of the Assumption
Most theoretical models for quantifying the temperature evolution in post-flashover
fires are based on the assumption of uniform compartment temperatures [2], which
is also referred to as the well stirred reactor assumption. This is the case for both
analytical models and zone models. Karlsson and Quintiere [1] note that this
assumption, among others, is required for an analytical solution of the energy
balance for the compartment. In particular they note that the methods of
Magnusson and Thelandersson in 1970 [3] and Babrauskas and Williamson in 1978
[4] adopted this approach. The former is the basis for the Eurocode parametric
temperature time curve [1]. Drysdale [5] notes that a justification of this assumption
often used is that there is supposedly a small gradient in the vertical temperature
13
distribution during a post-flashover fire and even smaller horizontal gradients. For
example, a single test from 1975 is cited showing a nearly uniform vertical
temperature distribution at one moment at the onset of flashover [5]. However, this
justification has not been evaluated any further. Furthermore, due to the limited
number of thermocouple trees in most fire tests (typically one or two), the presence
of horizontal gradients cannot be investigated and is rarely reported.
Franssen proposed modifications to the Eurocode parametric temperature-time
curve to better correlate the predicted peak temperatures with those from 48
experiments [6]. However, dispersions of the temperature data about the
compartment averages for the experiments are not given, presumably because the
assumption of temperature uniformity was automatically invoked.
The uniform temperature assumption is fundamentally inherent in the test methods
used for classifying structural fire resistance. The fire rating system adopted by most
building codes and standards worldwide is based on single elements of construction
being subjected to furnace tests in which the gas temperature evolution follows that
of a uniform standard fire. It is a key aim of these tests to produce as uniform a
temperature field as possible throughout the furnace. Typical furnace tests include
about four to nine thermocouple or plate thermometer measurements in different
locations. ISO 834 [7] specifies the compartment temperature as the spatial average
from all of the thermocouples monitoring the gas phase. The test requires that each
individual thermocouple be within 100°C of the standard fire temperature-time
curve specified at all times after the initial 10min. The test also requires that the
percentage difference between the areas under the measured compartment average
and the standard temperature-time curves be within 15% of each other after the first
10min, 10% after 30min, 5% after 60min, and 2.5% thereafter. BS 476 [8] and ASTM
E119 [9] have similar tolerances.
14
The tight tolerances required in standard fire tests are specifically set to ensure that
the temperature field in the compartment is uniform. While standard fire curves
have been criticised before on many counts for not representing natural fires [5, 6,
10], the spatially homogeneous temperature assumption has not typically been one
of them.
2.2.2 Critiques of the Assumption
Harmathy [11] presents a qualitative critique of the homogeneous temperature
assumption, also referred to as the well stirred reactor assumption. The critique
states that external flaming close to a vent invalidates the well stirred reactor model.
Harmathy suggests division of the compartment into three zones to allow
mathematical treatment: a zone of primarily fresh incoming air, a zone dominated
by the presence of the flame, and a zone behind the flame with mixed pyrolyzates
and combustion products. According to this classification, the homogeneous
temperature distribution would only be valid in this last zone. However, this
critique does not provide any quantification of the heterogeneity or its effects.
Bøhm and Hadvig [12] reported differences in experimental temperature
measurements of 200 to 500°C within a single post-flashover fire, with the hottest
temperatures in the centre of the compartment. Their test compartment was 4.6m x
4.6m x 2.5m, and temperature measurements were made at eight different locations.
The temperature differences led to difficulties in predicting the heat fluxes to both
the fuel surface and the exposed structure, but no further analysis was made of the
effect of the non-uniformity.
Welch et al. [13] and Abecassis et al. [14] reviewed the experimental data of the
Cardington Tests and the Dalmarnock Fire Tests, respectively, in terms of
temperature and heat flux fields and concluded they did not support the
conventional assumption of uniformity. These tests are described in Section 2.3.3.
15
2.3 Experimental Review
The presence of considerable temperature gradients during post-flashover fires has
previously been observed, although not systematically examined. Tests in large or
irregularly shaped compartments and real fires can provide insight into the
potential dispersion of temperatures and are reviewed here.
2.3.1 Non-Uniform Burning in Experiments
Kirby et al. [15] ran a test series burning wood cribs in a long enclosure with
approximate dimensions of 22.9m long x 5.6m wide x 2.8m high. All of the tests
were ignited at the rear, except one in which all wood cribs were ignited
simultaneously. The results of all tests show that the fire moved relatively quickly
from the ignition location to the front of the compartment, where the vent was
located. After the fuel in the front of the compartment burnt out, the fire
progressively travelled back into the compartment and ultimately consumed all the
fuel and self-extinguished at the rear. Temperature results of Test 1 from this test
series are shown below in Figure 2.1 at the rear, middle and front of the
compartment.
Thomas and Bennetts [16] conducted a test series of ethanol pool fires in a small
rectangular enclosure (1.5m x 0.6m x 0.6m) to determine the influences of ventilation
size and location on the burning rate. They found that there were significant
differences in burning rates between having the opening on the short end (long
enclosure) or the long side (wide enclosure). They observed temperature differences
at different locations up to 500°C, generally with greater temperatures nearer the
vents, as this is where the flames resided more often. This work was continued
further [17] with another experimental series of pool fires in a larger, long enclosure
(8m x 2m x 0.6m), in which the opening size on the short end was varied. The results
obtained were similar to both their earlier work [16] and that of Kirby et al. [15].
16
They conclude that a structural element near the vent would be exposed to more
severe conditions than one further inside the compartment.
Figure 2.1: Comparison of temperature-time measurements at three different locations,
spaced 8m apart, from the rear to the front of the compartment, illustrating non-
uniform burning during of wood cribs during the tests of Kirby et al. [15].
2.3.2 Travelling Fires
Since the scale of most enclosures in real buildings is significantly larger than the
scale in the few experimental tests available, it is likely that even higher degrees of
non-uniformity are to be expected in real fires. The real, large fires in the World
Trade Center towers 1, 2 [18] and 7 [19] in New York in September 2001, the
Windsor Tower in Madrid, Spain in February 2005 [20] and the Faculty of
Architecture at TU Delft in the Netherlands in May 2008 [21] were all observed to
travel across floor plates. Due to the travelling nature of the fires, it is likely that
temperature distributions during these events were highly non-uniform. While no
data exist to validate this, extensive numerical simulations conducted for the World
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Tem
pe
ratu
re (°
C)
Time (min)
Rear
Middle
Front
17
Trade Center investigations by NIST clearly show temperature variations within
single compartments of several hundred degrees Celsius [18, 19].
2.3.3 Fire Tests with High Spatial Resolution
Traditionally, most fire tests have only limited spatial resolution in temperature
measurements. For example, the series of well ventilated fire tests conducted by
Steckler et al. [22], which are often cited in fire model validation studies, monitored
the vertical distribution of gas temperatures at only two locations; at the vent and at
one internal corner of the compartment. This low spatial resolution cannot provide
the necessary insight into the degree of temperature homogeneity and leaves the
uniformity assumption unchallenged.
More recent tests, such as the Dalmarnock Fire Tests [23, 14] in 2006 and the Natural
Fire Safety Concept 2 test series at Cardington [24, 13] in 1999, have included a
much greater spatial resolution of instrumentation. General overviews of these
experimental setups are provided here.
The Dalmarnock Fire Tests, which provide the greatest instrumentation density to
date, were conducted in a real high-rise apartment building in Glasgow, UK [23, 14].
The two tests conducted had a realistic fuel load of typical residential/office
furnishings. The compartment was 4.75m x 3.50m x 2.45m, containing 20
thermocouple trees, each with 12 thermocouples (placed 0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.6,
0.8, 1.0, 1.3, 1.6 and 2m from the ceiling). The Dalmarnock experimental layout is
given in Figure 2.2. Ignition occurred in the waste-paper basket adjacent to the sofa.
Two tests were conducted, however only Test One is examined as the fire in the
second test was manually suppressed before flashover.
18
Figure 2.2: Experimental layout of the Dalmarnock Test One [23, 14]. Locations of the 20
thermocouple trees (each with 12 thermocouples in height) are noted by blue
crosses.
The eight Cardington Tests were conducted in a room 12m x 12m x 3m with
uniformly spaced fuel load packages distributed across the floor [24, 13]. Sixteen
thermocouple trees containing four thermocouples each were placed on a uniform
grid in the compartment to record the gas temperatures, shown in Figure 2.3. The
tests were conducted with various combinations of fuel type, ventilation
distribution, and interior lining material. The tests had liquid fuel channels
connecting the fuel packages so that ignition and the subsequent burning could be
as uniform as possible.
4.75m
3.5m
19
Figure 2.3: Experimental layout of Cardington Tests [24, 13]. Locations of the 16
thermocouple trees (each with 4 thermocouples in height) are noted by black
dots.
The Cardington experiments intended to test two types of compartment insulation;
“insulating” (I) and “highly insulating” (HI). However, after Test 1 the “highly
insulating” material was placed on the ceiling for all remaining tests, creating an
intermediate level of insulation (I+). The fuel packages were either just wood cribs
(W) or a combination of wood and plastic cribs (W+P). The ventilation openings
were either fully open on the front (F) of the enclosure or on the front and back
(F+B). A summary of these parameters for all eight tests is given in Table 2.1.
Test Number 1 2 3 4 5 6 7 8
Fuel Type W W W+P W W+P W W+P W+P
Insulation Type I HI HI HI HI I+ I+ I+
Opening Location F F F F+B F+B F+B F+B F
Table 2.1: Summary of test conditions in Cardington [24, 13].
Both data sets have a sufficient number of data points to allow for representative
statistical analyses. Dalmarnock had 240 points and the Cardington Tests each had
64. The Dalmarnock tests have both well distributed measurement points and a high
12m
12m
20
density of instrumentation (5.9 thermocouples/m3). The Cardington Tests had well
distributed measurement points, but not a high density of instrumentation
(0.15 thermocouples/m3).
The Dalmarnock test data were corrected for thermocouple radiation errors using
the method of Welch et al. [13]. The Cardington data have not been corrected.
However, Welch et al. [13], using Cardington Test data, report that typically
corrections fall in the range of 10 – 40°C, with occasional values as high as 100°C for
flame temperatures. Additional calculations were performed using the
thermocouple corrections for one of the Cardington Tests to confirm that similar
results were obtained to those presented in this study.
The results from Dalmarnock Test One are given in Figure 2.4. The results are
shown with the average compartment temperature and standard deviation in the
shaded region, plus the maximum and minimum temperature measurements in the
compartment at any given time. Two distinct post-flashover periods can be
observed in the Dalmarnock data. The change between the first and second period is
caused by window breakage at approximately 13.5 minutes after ignition. The
spatial location of the hot and cold spots can be investigated tracking the maximum
and minimum temperature curves. Through the test, the maximum temperature
was registered at different times in 52 thermocouple locations, distributed over 16
out of the 20 thermocouple trees and all but one of the 12 heights. No particular
pattern of where the peak temperatures were located is observed. The minimum
temperature was registered at only three different thermocouple locations
(thermocouple trees 4, 6, and 18 shown in Figure 2.2) all at the lowest thermocouple
(0.45m above the floor). All three locations are near pathways for make-up air to the
fire compartment.
21
Figure 2.4: Experimental results of Dalmarnock Test One [23, 14] showing the
compartment average, maximum and minimum temperatures, and the
standard deviation. Flashover occurred at 5min, window breakage at 13.5min,
and the fully developed fire lasted until suppression at 19min.
The results for all eight of the Cardington Tests are shown in Figure 2.5. Note that
there was a period between 16 and 22 min of Cardington Test 1 where data
collection was temporally lost (interpolation is provided).
The general results are summarised in Table 2.2 which provides the minimum,
mean, and maximum standard deviations, as well as the maximum average
compartment temperature reached for each test. The standard deviations are only
included for portions of the tests where the average compartment temperatures are
above 500°C, as the interest of this examination lay in the post-flashover portion of
the experiments. Table 2.2 also presents averaged values for two different furnace
tests conducted on the same wall assembly to the ASTM E119 standard fire in April
2009 [25]. The tests, carried out at a commercial laboratory to provide a rating for a
bespoke wall assembly, included nine gas phase thermocouples.
0
200
400
600
800
1000
0 5 10 15 20
Tem
pe
ratu
re (°
C)
Time (min)
Avg
ssss
Max
Min5 min
13.5 min
19 min
22
Figure 2.5: Experimental results of the Cardington Tests [24, 13] showing compartment
average, maximum and minimum temperatures, and the standard deviation for
each test. See Table 2.1 for a summary of conditions for each test.
Cardington 1
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 2
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 3
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 4
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 5
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 6
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 7
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
Cardington 8
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Time (min)
Temperature (°C
)
23
Test Min � (°C)
Mean � (°C)
Max � (°C)
Max ���� (°C)
Dalmarnock Test One 105 132 233 733
Cardington 1 38 84 136 857
Cardington 2 31 83 153 1075
Cardington 3 31 100 208 1103
Cardington 4 31 52 93 1199
Cardington 5 18 56 135 1147
Cardington 6 25 44 129 1218
Cardington 7 20 51 159 1200
Cardington 8 32 83 213 1107
Standard Fire Tests 8 12 39 N/A
Table 2.2: Summary of the temperature measurements of each spatially resolved fire test
and the mean values of two standard fire tests to ASTM E119.
In addition to the values shown in the Table 2.2, peak local temperatures range from
23% (Cardington Test 6) to 75% (Dalmarnock Test One) higher than the
compartment average, with a mean peak increase of 38% across all tests. Local
minimum temperatures range from 29% (Cardington Test 4) to 88% (Dalmarnock
Test One) below the compartment average, with a mean local minimum
temperature of 49% across all tests.
Higher mean standard deviations are observed in Dalmarnock Test One (132°C)
than all of the Cardington Tests (mean of 70°C). This is to be expected for several
reasons:
• Dalmarnock Test One had a much higher density of instrumentation than
the Cardington Tests, making it more likely that the full range of
temperature conditions was recorded.
• The thermocouple layout in Dalmarnock Test One covered regions with fuel
packages and regions remote from fuel packages. In Cardington, all
thermocouples were located above fuel packages and thus the data have a
bias towards flame temperatures.
24
• There were only four different thermocouple heights in the spacing of the
Cardington Tests, all relatively high, compared to the twelve in Dalmarnock,
which were evenly distributed. Thus the Cardington data are biased towards
temperatures in the upper portion of the compartment.
• The Dalmarnock Test had a realistic fire scenario where real-world
furnishings were arranged in a non-uniform manner and one ignition point
was used. In contrast, the Cardington Tests had well distributed fuel
packages ignited simultaneously.
A clear trend can be seen in the results from Cardington. Tests 4 through 7 all have
lower standard deviations (mean of 51°C) than Tests 1, 2, 3, and 8 (mean of 88°C).
The key difference between the two groups of tests is the ventilation position. Tests
1, 2, 3, and 8 had ventilation only on one side of the compartment, while Tests 4
through 7 had ventilation at two opposing sides. This fact is in line with the results
obtained by the studies previously highlighted with long enclosures [15, 16, 17].
Thus there is heterogeneity in the temperature field due to the depth of the
compartment relative to the position of the vents. This effect is less obvious for the
tests with ventilation on opposing sides.
These results confirm that there is considerable heterogeneity in the temperature
field of post-flashover fires. Real world fires are likely to have a level of dispersion
in the temperature field closer to that measured in Dalmarnock Test One than those
of the Cardington Tests. This is because the high density of instrumentation in
Dalmarnock recorded more of the temperature field than those in the Cardington
Tests, thus a more complete depiction of the variation was established. Furthermore,
the fuel types and distributions of real world fires that can cause heterogeneity are
more likely to match those of Dalmarnock than the uniformly spaced cribs of
Cardington.
25
It is also worth noting that the tests examined were conducted in compartments of
dimensions that are consistent with the homogeneous temperature assumption.
Thus other compartments with larger or more complex geometries will show
broader temperature dispersions.
2.3.4 Data Distributions
Examination of the statistical distributions of the data from each test provides more
insight into the level of uniformity of the temperature field. Figure 2.6 presents the
data distributions for four different times of Dalmarnock Test One with the
corresponding normal distribution overlaid. The distributions are shown at four
times, evenly spaced between flashover and suppression. The temperature
measurements are grouped into 40°C bands, as to encompass the experimental
uncertainty. If the homogeneous temperature assumption held, there would only be
one bar at any given time.
Figure 2.6: Comparisons of the measured temperature distributions against the associated
normal distributions after flashover for Dalmarnock Test One.
5 min after Flashover (10 min)
0
0.05
0.1
0.15
0.2
0 200 400 600 800 1000 1200
Temperature (°C)
Probability
1 min after Flashover (6 min)
0
0.05
0.1
0.15
0.2
0 200 400 600 800 1000 1200
Temperature (°C)
Probability
Data
Normal Distribution
13 min after Flashover (18 min)
0
0.05
0.1
0.15
0.2
0 200 400 600 800 1000 1200
Temperature (°C)
Probability
9 min after Flashover (14 min)
0
0.05
0.1
0.15
0.2
0 200 400 600 800 1000 1200
Temperature (°C)
Probability
26
Figure 2.7 and Figure 2.8 provide details for the data distributions of the Cardington
Tests. Figure 2.7 presents the data distributions for the four Cardington Tests with
ventilation at one side only (F), while Figure 2.8 presents the data distributions with
ventilation on opposing sides (F+B). The F data show a greater span in the
distributions than the F+B data.
The test data have been presented with standard deviations as a measure of the
departure from uniform temperature conditions. For a simplified estimation of the
meaning of the standard deviation, it is noted that approximately 65% of all data fall
within the span between one standard deviation on either side of the average and
approximately 95% fall within the same span of two standard deviations.
While the data distributions shown in Figures 2.6 through 2.8 do not always fit
normal distributions, at most times for most tests they are sufficiently close to treat
the data as normally distributed for the purposes of this analysis.
2.3.5 Standard Deviation vs. Temperature Rise
Figure 2.9 shows the relationship between the normalised standard deviation, σ�, and the average temperature rise from ambient, ∆�� . Each data point represents
one instant in time, with one point taken every minute for each test. The normalised
standard deviation, ��, is defined as the standard deviation divided by the average
compartment temperature rise above ambient, ∆�� . The Cardington Tests have
been divided into the two ventilation groups previously noted. Cardington F is the
group with ventilation in the front only and Cardington F+B is the group with
ventilation from both the front and back.
27
Figure 2.7: Comparisons of the measured temperature distributions against the associated
normal distributions for Cardington Tests with ventilation on one side only
(Tests 1, 2, 3 and 8).
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 8
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 3
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 2
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 1
28
Figure 2.8: Comparisons of the measured temperature distributions against the associated
normal distributions for Cardington Tests with ventilation on opposing sides
(Tests 4, 5, 6 and 7).
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 7
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 6
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 5
50 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
30 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
10 min
0
0.1
0.2
0.3
0.4
0 200 400 600 800 1000 1200 1400
Temperature (°C)
Probability
Cardington 4
29
Figure 2.9: Observed relationship between the normalised standard deviation vs.
temperature rise in the spatially resolved fire tests available.
These results indicate that there are significant heterogeneities in the gas field across
the whole range of temperatures. Furthermore, the scatter shows a clear trend; the
higher the temperature, the lower the normalised standard deviation. The
maximum temperature rise, just above 1200°C, marks the peak flame temperature
rise above ambient, which is at the upper end of temperature rises possible in a
typical post-flashover fire. More intense fires lead to hotter and more uniform
conditions in their enclosures, whereas in less intense fires the flame and smoke
regions dominate less of the gas field and less uniformity is observed. A clear
difference can be seen in the ventilation effect between the two groups from the
Cardington Tests, with the Cardington F Tests having less homogeneity than
Cardington F+B Tests. Also the greater degree of heterogeneity from the
Dalmarnock test can be seen.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 200 400 600 800 1000 1200
σ' (°C
/°C
)
ΔTavg (°C)
Dalmarnock
Cardington F
Cardington F+B
Middle of Envelope
30
The shaded region represents an approximate envelope for all of the data points.
The best fit equation for the curve that runs through the middle of this envelope is
given in Eq. (2.1).
�� = �∆�� = 1.939 − 0.266���∆�� � (2.1)
This curve could be used as a nominal expression of the standard deviation for any
temperature-time curve. The shaded envelope could be expected to apply to fires in
compartments of similar sizes as those assessed in this paper. For fires in
compartments of a much larger size, such as the real ones previously cited [18, 19,
20, 21], the temperature field will likely be much more non-uniform and a travelling
fire should be expected. A general discussion of the temperature fields in travelling
fires is available in the literature [26, 27].
The middle of the envelope has been used in lieu of a regression analysis because
the data are biased towards the Cardington Tests due to the large number of data
points for each test. There were eight Cardington Tests and each lasted longer than
Dalmarnock Test One. Therefore the shaded envelope was used to eliminate any
bias towards the Cardington data. For the reasons already discussed, the
Cardington data are deemed inappropriate to express standard deviations for a
general, real fire scenario.
2.4 Effect of Temperature Heterogeneity on the
Structure
Structural fire resistance calculations are routinely based on averaged temperature
values determined on the basis of standard fire tests conducted in test furnaces
which are explicitly intended to ensure uniform gas phase temperatures. However,
recent studies have shown that the behaviour of certain structural elements are
31
affected by temperature gradients [28, 29], thus there is a motivation to revisit the
homogeneous temperature assumption. Moreover, the experimental results
analysed above are at odds with the traditional assumption of temperature
uniformity, thus the effect of this heterogeneity on the heating of structural elements
is reviewed here.
A simplistic method for assessing the impact of non-uniform temperature
distributions on single structural elements has been adopted. These calculations are
intended to provide insight into the performance of simple structures and are not
proposed to be a design methodology or calculation guideline. Further research is
required to determine true structural response to non-uniform heating as the
analysis of the fire test data indicates that the use of a uniform temperature
distribution does not capture the true thermal environment of a real fire. Therefore
these simplistic calculations have only been adopted for illustrative purposes, to
examine trends for structures heated to temperatures above the compartment
average.
It is important to clarify that the impact of non-uniform temperature distributions
on full structural behaviour is not being assessed here, nor issues associated with
details of heat transfer such as soot concentrations or velocities. While these details
will have an impact on the heating of structural elements, they are not usually part
of standard thermal calculations for the purposes of structural fire analysis.
For illustrative purposes, three simplified examples of structural elements are used:
(1) an unprotected steel I-beam, (2) a protected steel I-beam fire rated to 60 min
using a generic insulation, and (3) a concrete beam with a 60 min fire rating. All
three beams, with dimensions given in Figure 2.10, nominally have the same design
bending moment capacity under ambient temperature. The beams selected for the
analysis are representative of typical beams covering the most common construction
types and range of thermal inertias found in real buildings. The unprotected and
32
protected steel beams have the same dimensions, except that an additional layer of
fire protection is applied to the protected beam (12 mm of high density perlite
insulation). It is assumed that a concrete floor slab is present above the beams such
that they are only heated on three sides.
Figure 2.10: Dimensions of the steel (left) and concrete (right) beams used to determine
representative structural responses to the varying temperature distributions.
The thermal response of each beam was calculated for a variety of temperature-time
curves above the mean. This information was used in conjunction with thermal
definitions of fire resistance based on assumed critical temperatures for each
material. Each curve was generated from each experimental data set, starting with
the average compartment temperature-time curve, and then adding a fraction of the
standard deviation to it, in units of one quarter of the standard deviation. Thus, the
first curve analysed for each beam from a given experiment was the average
compartment temperature-time curve. The next curve used was the average
compartment temperature-time curve plus one quarter of the standard deviation,
then the average compartment temperature-time curve plus one half of the standard
deviation, and so on until the average compartment temperature-time curve plus
two times the standard deviation. Figure 2.11 illustrates this by showing every
second curve used for Cardington 2.
400mm
300mm
30mm
32mm dia
16mm dia
8mm dia
Not to scale
15mm
15mm
8mm
200mm
350mm
33
Figure 2.11: Temperature-time curves for Cardington Test 2, ranging from the average
temperature-time curve (representing the 50th percentile) to the average
temperature-time curve plus two standard deviations (representing the 97th
percentile). Note that this plot only shows every other curve used for structural
assessment.
This approach allows the results to be viewed continuously from the average
compartment temperature-time curve through to the average compartment
temperature-time curve plus two standard deviations. This span, if viewed
cumulatively, covers the range between the 50th percentile and the 97th percentile.
Only values above the mean have been analysed here. This is to focus on the
possibility of current design practices underestimating the effect of fire on structures
by use of the average compartment temperature only. The non-uniformity will also
result in some elements of structure exposed to less severe conditions than currently
assumed using the compartment average. This is not considered here, as a common
aim of structural fire engineering is to err on the side of conservatism.
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Tem
pe
ratu
re (°
C)
Time (min)
Avg (50th Percentile)
Avg + 0.5σ (69th Percentile)
Avg + 1σ (84th Percentile)
Avg + 1.5σ (93rd Percentile)
Avg + 2σ (97th Percentile)
34
From the percentile temperature-time ranges developed, the peak temperature rise
and time to failure, based on an assumed critical temperature, were calculated for
each beam and each fire test as a function of the temperature percentile. The
unprotected steel beam temperature was calculated by lumped mass heat transfer,
as given by Buchanan [30]. The protected steel beam temperatures were also
calculated by the lumped mass method given by Buchanan. For the concrete beam,
the temperature calculated was that of the internal steel reinforcing bars, assumed to
be at the same temperature as the concrete adjacent to it, i.e. the temperature at the
extreme underside of the bars. This in-depth temperature of the concrete was
calculated with a one-dimensional finite-difference method in explicit form, as given
by Incropera et al. [31].
The time to failure is taken as the time for the steel to heat to 550°C, as this is
normally considered an approximate temperature above which steel loses sufficient
strength such that failure of a typical simply-supported beam could occur under the
loads assumed to be applied during a fire [5]. Higher temperatures are sometimes
used; however 550°C is selected here for the purpose of these calculations, for both
steel beam and rebar temperatures.
A full description of the calculation methods used is given in Appendix A. It is
acknowledged that the calculations and failure criterion are simplistic, and it is
important to note that the illustrative approach taken herein does not account for
several important issues related to the heating and ultimate response of the
structure.
Normalised results for the maximum temperature rise reached against the
temperature percentile are shown in Figure 2.12 for all three beam types. The
normalised temperature rise, ∆′, is defined as the steel temperature rise when
exposed to the given temperature percentile curve divided by the steel temperature
rise when exposed to the average temperature-time curve. The resultant hotter steel
35
temperature would not be calculated if only the average compartment temperature
were considered. The standard fire is included using the normalised standard
deviation in Eq. (2.1) to generate the full range of temperature-time curves. For
guiding purposes, note that if the gas phase were completely homogeneous, a
horizontal line at ordinate 1 would be shown.
The results show that the increased temperatures associated with the non-
uniformity have a potentially important impact on the structural performance of the
beams analysed. Tables 2.3 through 2.5 show the results for temperature rise and
time to failure for the 80th percentile temperature-time curves (equivalent to the
average compartment temperature-time curve plus 0.85 times the standard
deviation) for each experiment and the standard fire when compared to the average
compartment temperature-time curve. Note that 80th percentile values are often
recommended in fire safety engineering for design. For example, in the UK PD7974
recommends fire loads for structural fire analysis to be the 80th percentile values
[32].
Compared to the calculations using the average compartment temperature
measurements, the results at the 80th percentile show that a higher temperature
region in a compartment could result in a steel temperature rise up to 25% higher
(15% for the unprotected steel beam, 18% for the protected steel beam, and 25% for a
concrete beam) or reach the time to failure, i.e. the fire resistance time, up to 31%
faster (31% for the unprotected steel beam, 15% for the protected steel beam, and
22% for the concrete beam). For the 95th percentile, temperature rises can be up to
60% higher and fire resistance times 55% shorter.
36
Figure 2.12: Results of the normalised temperature rise for each type of beam analysed.
Note that a horizontal line at abscissa 1 would represent a homogeneous
temperature field.
1
1.1
1.2
1.3
1.4
1.5
1.6
50 60 70 80 90 100
ΔT
' (°° °°C
/ °° °°C
)
Temperature Percentile
Unprotected Steel
Dalmarnock
Cardington F
Cardington F+B
Standard Fire
1
1.1
1.2
1.3
1.4
1.5
1.6
50 60 70 80 90 100
ΔT
' (°° °°C
/ °° °°C)
Temperature Percentile
Protected Steel
1
1.1
1.2
1.3
1.4
1.5
1.6
50 60 70 80 90 100
ΔT
' (°° °°C
/ °° °°C
)
Temperature Percentile
Concrete
37
Temperature Rise Time to Failure
Test Difference % Increase Difference % Decrease
Dalmarnock Test One 96°C 15% 3.8 min 26%
Cardington 1 91°C 11% 4.5 min 21%
Cardington 2 87°C 8% 1.0 min 6%
Cardington 3 84°C 8% 1.1 min 15%
Cardington 4 44°C 4% 0.5 min 5%
Cardington 5 61°C 5% 0.5 min 5%
Cardington 6 44°C 4% 0.7 min 4%
Cardington 7 59°C 5% 0.5 min 8%
Cardington 8 109°C 10% 0.9 min 9%
Standard Fire 81°C 8% 3.1 min 31%
Table 2.3 Summary of the unprotected steel beam results for temperature rise and time to
failure for the 80th percentile temperature-time curve.
Temperature Rise Time to Failure
Test Difference % Increase Difference % Decrease
Dalmarnock Test One 30°C 18% Did not fail Did not fail
Cardington 1 43°C 12% Did not fail Did not fail
Cardington 2 51°C 8% 5.2 min 10%
Cardington 3 59°C 10% 5.6 min 12%
Cardington 4 29°C 5% 3.1 min 7%
Cardington 5 36°C 6% 6.4 min 13%
Cardington 6 25°C 4% 2.6 min 5%
Cardington 7 31°C 5% 3.7 min 9%
Cardington 8 52°C 9% 5.3 min 11%
Standard Fire 71°C 10% 8.9 min 15%
Table 2.4 Summary of the protected steel beam results for temperature rise and time to
failure for the 80th percentile temperature-time curve.
Temperature Rise Time to Failure
Test Difference % Increase Difference % Decrease
Dalmarnock Test One 47°C 25% Did not fail Did not fail
Cardington 1 53°C 14% Did not fail Did not fail
Cardington 2 60°C 10% 7.0 min 13%
Cardington 3 67°C 12% 6.5 min 15%
Cardington 4 34°C 6% 2.8 min 8%
Cardington 5 48°C 9% 5.6 min 14%
Cardington 6 33°C 5% 2.5 min 6%
Cardington 7 40°C 7% 3.0 min 9%
Cardington 8 66°C 11% 6.7 min 15%
Standard Fire 63°C 9% 15.3 min 22%
Table 2.5 Summary of the concrete beam results for temperature rise and time to failure
for the 80th percentile temperature-time curve.
38
With respect to the heat transfer analysis, the methods used are analogous to those
employed for uniform temperature fields, but because they are applied to a range of
temperature-time curves above the compartment average, the cumulative results
provide insight into the possible heating from heterogeneous temperature fields. It
is noted that fully spatially resolved heat transfer analyses, as described by Jowsey
[28], were not conducted. That type of analysis could be applied to calculate the
non-uniform heating from a heterogeneous temperature field, but requires spatially
resolved optical properties and velocities of the combustions gases, which were not
available for all of the tests reviewed in this paper.
In terms of the structural behaviour, only a single element has been considered with
a fixed temperature representing the failure criterion, thus the method ignores a
range of possible structural behaviours including axial restraint, membrane actions,
and flexural continuity over multiple spans in a real building. Many more detailed
methods and criteria exist to determine the impact of fire on structures for defining
their fire resistance [30]. However, given that generic structural elements are being
assessed for illustrative purposes only, the current analysis provides useful insights.
Although not assessed here, the location of the thermal non-homogeneities along a
structural member is potentially important, since localised heating in regions of
lower applied stresses may be less critical for structural performance than in regions
of high applied stress. A more detailed structural analysis accounting for thermal
non-homogeneities would be required to investigate the potential impacts of non-
uniform heating on full frame response to fire.
2.5 Conclusions
The statistical analyses of the fire tests examined show that there is considerable
non-uniformity in the temperature fields of real post-flashover fires. Peak local
temperatures range from 23% to 75% higher than the compartment average, with a
39
mean peak increase of 38%. Local minimum temperatures range from 29% to 88%
below the spatial average, with a mean local minimum temperature of 49% below
the compartment average. This is in contrast to the common assumption of a
homogeneous temperature field often used in quantification and modelling of post-
flashover compartment fires.
The contradictions between the assumption of homogeneity and measured
heterogeneity means that fire tests with limited spatial instrumentation, which are
often only reported as average temperature measurements, may lead to erroneous
conclusions. If fire tests are not well instrumented, it may be difficult to determine
which portion of the temperature distribution has been measured and which parts
were not recorded. It has been shown here with the data from the most densely
instrumented experiments to date that this range is on the order of hundreds of
degrees Celsius.
This heterogeneity can have a potentially non-negligible impact on the structural
fire resistance of steel or concrete beams. This is noticeable in increased structural
temperatures (up to 25% higher) and shorter times to failure (up to 31% faster) at the
80th percentile values compared to those that would be calculated assuming the
average compartment temperature. These results along with the recent studies
showing some structural elements are adversely affected by temperature gradients
gives motivation to revisit the homogeneous temperature assumption and further
explore its ramifications.
While the full implications of the temperature heterogeneity of post-flashover fires
are not explored here, it is apparent that post-flashover fires do not reach uniform
conditions. The presented results highlight the need to increase the spatial
resolution of measurements in fire experiments to capture the full variation within
the compartment. Spatially resolved data can lead to a rational statistical approach
40
to fire behaviour when applied to fire safety and structural engineering
applications.
References
1 Karlsson, B. and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.
2 Thomas. P.H., “Modelling of compartment fires,” Fire Safety Journal, Vol. 5,
1983, pp. 181 – 190.
3 Magnusson, S.E. and Thelandersson, S., “Temperature-time curves for the
complete process of fire development — a theoretical study of wood fuels in
enclosed spaces,” Acta Polytechnica Scandinavica, Stockholm, Vol. Ci 65, 1970.
4 Babrauskas, V. and Williamson, R.B., “Post-flashover compartment fires: Basis
of a theoretical model,” Fire and Materials, Vol. 2, 1978, pp. 39–53.
5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.
6 Franssen, J.M. “Improvement of the parametric fire of eurocode 1 based on
experimental test results,” Proceedings of the 6th International Symposium on Fire
Safety Science, pp. 927–938, 1999. doi:10.3801/IAFSS.FSS.6-927.
7 ISO 834-1: Fire-resistance tests - Elements of building construction, Part 1: General
Requirements. ISO, 1999.
8 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:
Method for Determination of the Fire Resistance of Elements of Construction:
BSI, 1987.
9 ASTM E119 - 08a, Standard Test Methods for Fire Tests of Building Construction and
Materials. ASTM, 1987.
10 Keltner, N.R., Beck, J.V., and Nakos, J.T., “Using directional flame
thermometers for measuring thermal exposure,” ASTM E5 - Advances in the
State of the Art of Fire Testing, Miami, Florida, 2008.
11 Harmathy, T.Z., “Postflashover fires - an overview of the research at the
national research council of canada (nrcc), 1970-1985,” Fire Technology, vol. 22,
pp. 210–233, Aug. 1986.
41
12 Bøhm, B. and Hadvig, S., “Nonconventional fully developed polyethylene and
wood compartment fires,” Combustion and Flame, vol. 44, no. 1-3, pp. 201 – 221,
1982.
13 Welch, S., Jowsey, A., Deeny, S., Morgan, R., and Torero, J.L., “BRE large
compartment fire tests–characterising post-flashover fires for model
validation”. Fire Safety Journal, vol. 42, pp. 548 – 567, 2007.
14 Abecassis-Empis, C., Reszka, P., Steinhaus, T., Cowlard, A., Biteau, H., Welch,
S., Rein, G., and Torero, J.L., “Characterisation of Dalmarnock fire test one,”
Experimental Thermal and Fluid Science, Vol. 32, pp. 1334 – 1343, 2008.
15 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,
“Natural Fires in Large Scale Compartments”, British Steel, 1994.
16 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation
Openings – Comparison of Long and Wide Enclosures,” The 6th International
Symposium on Fire Safety Science, Poitiers, France, 1999.
doi:10.3801/IAFSS.FSS.6-941.
17 Thomas, I., Moinuddin, K., and Bennetts, I., “Fire development in a deep
enclosure,” The 8th International Symposium on Fire Safety Science, Beijing, China,
2005.
18 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,
Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the
World Trade Center Towers. NIST NCSTAR 1-5, 2005.
19 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,
Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire
Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST
NCSTAR 1-9, 2008.
20 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based
analysis of a concrete building subjected to fire,” Advanced Research Workshop on
Fire Computer Modelling, Santander, Spain, 2007,
http://www.era.lib.ed.ac.uk/handle/1842/1988.
42
21 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT
Instituut voor Veilingheids – en Crisismanagement, 2008.
22 Steckler, K.D., Quintiere, J.G., and Rinkinen, W.J., Flow Induced by Fire in a
Compartment. NBSIR 82-2520, 1982.
23 Rein, G., Abecassis-Empis, G., and Carvel, R. Eds., The Dalmarnock Fire Tests:
Experiments and Modelling. School of Engineering and Electronics, University of
Edinburgh, 2007.
24 Lennon, T. and Moore, D., “The natural fire safety concept - full-scale tests at
Cardington,” Fire Safety Journal, Vol. 38, 2003, pp. 623 – 643.
25 Internal Report, Arup Fire, San Francisco. 2009.
26 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and
Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th
International Interflam Conference, London, UK, 2007.
http://www.era.lib.ed.ac.uk/handle/1842/1980
27 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach
to design fires for structural analysis of non-conventional buildings: A case
study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,
http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf
28 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, The
University of Edinburgh, 2006, http://www.era.lib.ed.ac.uk/handle/1842/1480.
29 Gillie, M., Röben, C., Ervine, A., and Kirkpatrick, S., “The effects of non-
uniform fires on structural behaviour,” Proceedings of the Fith International
Conference on Structures in Fire, Singapore, 2008.
30 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.
31 Incropera, F., DeWitt, D., Bergman, T., and Lavine, A., Fundamentals of Heat and
Mass Transfer. John Wiley & Sons, 2007.
32 PD7974-0:2002 Application of fire safety engineering principles to the design of
buildings — Part 0: Guide to design framework and fire safety engineering procedures.
BSI, 2002.
43
3 A Review of Travelling
Fires in Structural Analysis
3.1 Introduction
As architectural trends change and become more ambitious, they challenge the
bounds of traditional engineering methods. This is true for structural fire
engineering, where the fire scenarios most commonly used for the design of modern
buildings are based on traditional methods that assume uniform burning and
homogeneous temperature conditions throughout a compartment, regardless of its
size.
However, close inspection of accidental fires in large, open-plan compartments
reveals that they do not burn simultaneously throughout the whole enclosure.
Instead, these fires tend to move across floor plates as flames spread, burning over a
limited area at any one time. These fires have been labelled “travelling fires”.
44
The uniform burning and homogeneous temperature assumptions are at the root of
many of the existing methods’ limitations and have not been confirmed
experimentally for large compartments. The traditional methods were developed
based on small scale tests and, while they are known be of some validity for small
compartments, cannot be readily applied to large enclosures.
Developing new methods to enhance optimisation of structural fire design, by
obtaining a more accurate characterisation of actual building performance, requires
a realistic definition of potential fire scenarios. Specifically, incorporation of
travelling fires will be necessary to reflect the state-of-the-art knowledge of fire
dynamics in large spaces.
This paper reviews research focused on travelling fires in structural analysis. It
highlights the historical developments as well as current uses and examines both the
definition of the thermal environment as well as structural analyses based on
travelling fires.
3.2 Traditional Design Methods
The earliest attempts of testing to understand structural performance in fire led to
the standard temperature-time curve, first published in 1917 [1]. This curve and
associated test methods given in standards, such as BS 476 [2], ISO 834 [3], and
ASTM E119 [4], have formed the basis for the fire rating systems in most building
codes and standards worldwide. The curve came from collating the results of
various post-flashover fire tests into one idealised curve. The tests that fed into the
development of the standard fire were intended to represent worst case fires in
enclosures to determine if the structure could withstand burnout. However, these
tests were conducted and the standard fire created prior to much scientific
understanding of fire dynamics. Thus the standard fire, unlike a real fire, has a
45
relatively slow growth rate (which was largely driven by the usage of furnaces
heated by manually stoked wood fuel [1]), never reduces in temperature due to fire
decay, and is independent of building characteristics such as geometry, ventilation
and fuel load [1, 5, 6]. Furthermore, the standard fire does not accurately reflect the
nature of real fires which do not uniformly heat building elements [7].
As fire science matured, models of post-flashover fire behaviour were developed to
account for a better understanding of compartment fire dynamics based on tests
conducted in small enclosures. Most of the theoretical models developed were
based on the assumption of uniform compartment temperatures [8]. This is the case
for both analytical models and zone models. Karlsson and Quintiere [9] note that
this assumption, among others, is required for an analytical solution of the energy
balance for the compartment. In particular they note that the methods of
Magnusson and Thelandersson in 1970 [10] and Babrauskas and Williamson in 1978
[11] adopted this approach.
Pettersson et al. [12] developed a design guide, based on the work of Magnusson
and Thelandersson [10], for specifying the thermal environment to be used for
structural design. The guidance document provides a set of temperature-time
curves for various compartment ventilation factors, fuel loads, and compartment
linings. This work was further developed by Wickström [13] and became the basis
for the Eurocode parametric temperature-time curve [14], which is a widely used
method in structural fire engineering today.
While other methods exist [15, 16, 17, 18], they all assume homogeneous
temperature conditions and uniform burning throughout the fire compartment.
Drysdale [5] notes that a justification of the homogeneous temperature assumption
often used is that there is supposedly a small gradient in the vertical temperature
distribution during a post-flashover fire and even smaller horizontal gradients. For
example, a single test from 1975 is cited showing a nearly uniform vertical
46
temperature distribution at one moment at the onset of flashover. Section 3.3 of this
paper presents further critiques of this assumption.
While most of the traditional methods tend to look at full compartment
involvement, some methods have been developed to look at localised fires [14, 19]
that look at the impact of a fire on only part of a structure. Considering localised
fires is a relaxation of the uniform burning assumption. This is relevant to this
review paper, as a travelling fire is, in essence, a localised fire that moves. Howver,
the methods developed for localised fires have not considered elevated smoke
temperatures away from the fire as methods for travelling fires have (see Section
3.4).
Buchanan [20] and Law et al. [21] provide concise histories of the development
structural analysis methods for buildings exposed to fires. What is of relevance to
this review is the move from solely analysing single elements to that of whole frame
behaviour, which was largely driven by specific accidental fires and large scale
testing at Cardington. Travelling fires, which provide highly non-uniform and
transient heating in time over the full length of a large compartment, may have a
considerable impact on whole frame structural behaviour.
3.3 Limitations of the Uniform Burning
Assumption
The traditional methods have known limitations in their application. For example,
Eurocode 1 states that the parametric curves are only valid for compartments with
floor areas up to 500m2 and heights up to 4m, the enclosure must also have no
openings through the ceiling, and the compartment linings are restricted to having a
thermal inertia between 1000 and 2200J/m2s½K, which means that highly conductive
linings such as glass façades and highly insulating materials cannot be taken into
account. As a result, common features in modern construction like large enclosures,
47
high ceilings, atria, large open spaces, multiple floors connected by voids, and glass
façades are excluded from the range of applicability of the current methodologies.
A recent survey of buildings in Edinburgh, UK [22], underlines the implications of
these limitations on the applicability of design fires, particularly for modern
structures. For buildings built over a long period of time starting in the early 20th
century, 66% of their total volume falls within the limitations. However, in a newly
constructed, modern building that has open spaces and glass façades, only 8% of the
total volume is within the limitations. This suggests that modern building design is
increasingly producing buildings that contain compartments to which parametric
fires should not be applied.
Furthermore, as noted in Section 3.2, the traditional design methods for specifying
the thermal environment for structural analysis are based on an assumption of
uniform burning and temperature conditions. Stern-Gottfried et al. [23] have
reviewed this assumption by analysis of existing experimental data from well-
instrumented fire tests. Results show that dispersion from the spatial compartment
average is significant and that the assumption of uniform temperature conditions
does not hold well (see Section 3.3.1 for more details). While this review was
conducted for relatively small enclosures, the findings are likely to be more relevant
for large enclosures as the compartment size increases, the degree of heterogeneity
is expected to increase.
It is worth noting that the traditional methods assume that worst case conditions are
caused by ventilation controlled fires. However, a recent review by Majdalani and
Torero [24] of early CIB tests and the resulting analyses of compartment fire
behaviour done by Philip Thomas and others highlights that ventilation controlled
fires are unlikely in large enclosures and that they are not necessarily more
conservative for structural analysis than fuel bed controlled fires. Majdalani and
Torero note that while the different burning behaviour between ventilation and fuel
48
bed controlled fires was clearly stated in the original studies, ventilation controlled
fires have nonetheless been assumed to be the most severe case for design.
Buchanan [6] notes that post-flashover fires in open plan offices are unlikely to burn
throughout the whole space at once. Although limited experimental data exist on
fire spread and temperature homogeneity in large enclosures, examination of
specific tests and the study of accidental fires can provide insight into the fire
dynamics of larger enclosures.
3.3.1 Evidence from Experiments
The well instrumented tests conducted at Dalmarnock [25] and Cardington [26]
were shown to have large standard deviations (in excess of 200°C at times) within
the temperature field [23]. Additionally, peak local temperatures in these tests were
found to vary from 23% to 75% above the compartment spatial averages, and local
minimums ranged from 29% to 88% below the averages.
Kirby et al. [27] ran a test series burning wood cribs in a long enclosure with
approximate dimensions of 22.9m x 5.6m x 2.8m. All of the tests were ignited at the
rear of the compartment, except one in which all wood cribs were ignited
simultaneously. The results of all tests showed that the fire moved relatively quickly
from the ignition location to the front of the compartment, where the vent was
located. After the fuel in the front of the compartment burnt out, the fire
progressively travelled back into the compartment and ultimately consumed all of
the fuel and self-extinguished at the rear. Temperature results at the rear, middle
and front of the compartment of Test 1 from this series are shown in Figure 3.1.
Thomas and Bennetts [28] conducted a test series of ethanol pool fires in a small
rectangular enclosure (1.5m x 0.6m x 0.6m) to determine the influences of ventilation
size and location on burning rate. They found that there were significant differences
in burning rates between having the opening on the short end (long enclosure) or
49
the long side (wide enclosure). They observed temperature differences across
multiple locations of up to 500°C, generally with greater temperatures nearer the
vents, as this is where the flames resided more often. This work was continued
further [29] with another experimental series of pool fires in a larger, long enclosure
(8m x 2m x 0.6m), in which the opening size on the short end was varied. The results
obtained were similar to both their earlier work [28] and that of Kirby et al. [27].
They conclude that a structural element near the vent would be exposed to more
severe conditions than one further inside the compartment.
Figure 3.1: Comparison of temperature measurements over time at three different locations
from the rear to the front of the compartment, illustrating non-uniform burning
of the wood cribs during the tests of Kirby et al. [27].
All of the tests mentioned here show, even in relatively small scales, that fires travel
and do not burn uniformly throughout the whole test enclosure.
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Tem
pe
ratu
re (°
C)
Time (min)
Rear
Middle
Front
50
3.3.2 Evidence from Accidental Fires
Many large, accidental fires, such as those in the World Trade Center Towers 1, 2
[30] and 7 [31] in New York in September 2001, the Windsor Tower in Madrid,
Spain in February 2005 [32] and the Faculty of Architecture building at TU Delft in
the Netherlands in May 2008 [33] were all observed to travel across floor plates, and
vertically between floors, rather than burn uniformly for their duration. Similar
observations were made of the Interstate Bank fire in Los Angeles in 1988 [34] and
the One Meridian Plaza fire in Philadelphia in 1991 [35].
The travelling nature of the fire in Tower 2 at the World Trade Center is shown in
Figure 3.2, which gives the recorded observations of the fire location and burning
behaviour along the East Face [30]. It can be seen that the area of flaming shifts
dramatically on the floors of fire involvement, both horizontally across floors as well
as vertically between floors.
Other than the fires in Towers 1 and 2 of the World Trade Center, which ended at
the time of building collapse, all of the incidents listed above lasted for many hours.
The Interstate Bank fire was the shortest and lasted a little under four hours, at
which point it was controlled by fire fighters. The One Meridian Plaza fire was the
longest, which lasted for almost 19 hours as it burnt from the 22nd to the 30th floor,
where it was eventually controlled by a sprinkler system.
These fires, in addition to being visually observed as travelling, had durations that
are well in excess of the time periods associated with the traditional design
methods. This difference in time scales is primarily due to those methods assuming
uniform burning on one floor only. Therefore the traditional methods may be
underestimating exposure times as compared to the lengths of real fires, which in
turn could affect the structural heating.
51
Figure 3.2: Observed fire locations over different time periods on the East Face of WTC
Tower 2 [30], indicating a horizontally and vertically travelling fire.
Blue = observation not possible, White = no fire, Yellow = spot fire, Red = fire
visible inside, Orange = external flaming.
3.4 Pioneering Methods
To progress past the limitations of the traditional methods, it is necessary to develop
engineering techniques that account for travelling fires. This section reviews the
published methods utilising travelling fires.
3.4.1 Large Firecell Method - HERA New Zealand
As part of a long term research programme at HERA in New Zealand aimed at
understanding the behaviour of complete steel frames exposed to fire, Clifton [36]
produced a first of its kind report related to design using travelling fires. The report,
entitled “Fire Models for Large Firecells” and referred to as the Large Firecell
52
Method (LFM) in this paper, gave an approach to apply specific fire models to
develop temperature-time relationships for travelling fires through a “firecell”. By
Clifton’s definition, a firecell is essentially one compartment of a building. For
example, an open plan office floor would be a single firecell.
Clifton applied two different fire models to generate temperature-time curves and
created a set of rules on how these should be applied to “design areas” within the
firecell. Each design area of the firecell at any one time could be classified as one of
the following conditions: fire, preheat, smoke logged, or burned out. This is
illustrated in Figure 3.3 at a fixed moment in time.
Figure 3.3: Representation of a spreading fire in the LFM [36]. Reproduced with permission
from the author.
The temperature-time curves for the design areas were calculated by one of two
models given, both for ventilation controlled fires. Temperatures for the preheat and
delayed cooling (for after burnout) periods were taken to be between 200 and 675°C,
depending on the type of construction used in the first version of the report and
then subsequently modified to 400 to 800°C in the proposed changes to the
document.
53
In the first version of the LFM, Clifton set the size of each design area based on the
fuel load density. He suggested 50m2 for a fuel load under 500MJ/m2, 100m2 for fuel
loads between 500 and 1000MJ/m2, and 150m2 for fuel loads greater than 1000MJ/m2.
This was modified to have the design area be 50m2 for all fuel loads in the proposed
changes. Windows were assumed to break once the adjacent gas temperature
reached 350°C. The rate of fire spread was based on the Kirby experiments [27]
highlighted in Section 3.3.1 and was specified to be 1m/s for well ventilated
conditions and 0.5m/s for less ventilation, as determined by the opening factor of
the case being examined.
Combining all of the various inputs in the method gives temperature-time curves at
any structural element. An example is shown in Figure 3.4.
Clifton acknowledged the challenges of developing this type of methodology. He
stated that no such method existed before and that there was a “paucity of
experimental data available”, which required “a crude and simplistic approach to
their development”. Therefore the model necessitated numerous assumptions
regarding fire size, ventilation conditions, fire spread, fuel distribution and fuel
type. Due to the assumptions needed, and the lack of experimental data, Clifton
stated that the LFM should mostly function as a research tool and should only be
used for single element checks in design.
Moss and Clifton [37] used the LFM in analysis of the large frame tests conducted at
Cardington. However, they noted that this method, combined with detailed
structural analyses led to results “that appeared to be realistic,” but “could not be
related to any directly comparable experimental results”. Further development or
applications of this method are not readily apparent in the literature.
54
Figure 3.4: Temperature-time curve of one design area in the LFM [36]. Reproduced with
permission from the author.
3.4.2 Travelling Fires Methodology – University of Edinburgh
The Travelling Fires Methodology (TFM), which has been developed by the authors
independently of the LFM over the last few years, incorporates travelling fires for
structural design. Full details of this method are given in Chapter 5 [38].
The TFM calculates the fire-induced thermal field such that it is physically-based,
compatible with the subsequent structural analysis, and accounts for the fire
dynamics relevant to the specific building being studied. In order to achieve this, a
fire model is selected that provides the spatial and temporal evolution of the
temperature field.
The fire-induced thermal field is divided in two regions: the near field and the far
field. These regions are relative to the fire, which travels within the compartment,
and therefore move with it. The near field is the burning region of the fire and
where structural elements are exposed directly to flames and experience the most
55
intense heating. The far field is the region remote from the flames where structural
elements are exposed to hot combustion gases (the smoke layer) but experience less
intense heating than from the flames. The near and far fields are illustrated in Figure
3.5. The near field region is analogous to the design area of the LFM.
Figure 3.5: Illustration of near and far fields in the TFM [38, 42].
Early work on the TFM in 2006 by Rein et al. [39] used Computational Fluid
Dynamics (CFD) to study both uniform and travelling fires in a multi-storey high
rise building, with atria connecting groups of three floors into “villages”. Later work
by Stern-Gottfried et al. [40] simplified and refined the method for a single floor,
utilising a ceiling jet correlation to generate far field temperatures. Jonsdottir et al.
[41] took this updated version and examined resultant steel temperatures.
Collaboration with structural fire engineers led to work [42] exploring the response
of a generic concrete frame to travelling fires, including a detailed sensitivity study.
Stern-Gottfried and Rein [38] then developed the methodology further by extending
the examination of the concrete frame via simplified heat transfer and identified the
critical parameters for applying the method to design.
The TFM does not assume a single, fixed fire scenario but rather accounts for a
whole family of possible fires, ranging from small fires travelling across the floor
plate for long durations with mostly low temperatures to large fires burning for
Far field (Tff) Near field (Tnf)
Near field
travels over
time
56
short durations with high temperatures. Using the family of fires enables the TFM to
overcome the fact that the exact size of an accidental fire cannot be determined a
priori. This range of fires allows identification of the most challenging heating
scenarios for the structure to be used as input to the subsequent structural analysis.
Each fire in the family burns over a specific surface area, denoted as ��, which is a
percentage of the total floor area, �, of the building, ranging from 1% to 100%.
Compared to this approach, the conventional methods only consider full size fires,
which are analogous to the 100% fire size in the TFM. All other burning areas
represent travelling fires of different sizes which are not considered in the
conventional methods.
The TFM assumes that there is a uniform fuel load across the fire path and the fire
will burn at a constant heat release per unit area typical of the building load under
study. From this the total heat release rate can be calculated by Eq. (3.1).
� = ��� " (3.1)
where � is the total heat release of the fire (kW)
�� is the floor area of the fire (m2)
� " is the heat release rate per unit area (MW/m2)
Furthermore, the local burning time over the fire area can be calculated by Eq. (3.2).
"# = $�� " (3.2)
where "# is the burning time (s)
$� is the fuel load density (MJ/m2)
57
Values typically used in the application of the TFM are 570MJ/m2 for the fuel load
density and 500kW/m2 for the heat release rate per unit area. This leads to a
characteristic burning time, "#, of 19min. This time correlates well to the free-
burning fire duration of domestic furniture, which Walton and Thomas [43] note is
about 20min. It is also in line with Harmathy’s [44] observation that fully developed,
well ventilated fires will normally last less than 30min.
Note that the burning time is independent of the burning area. Thus the 100%
burning area and the 1% burning area will both consume all of the fuel over the
specified area in the same time, "#. However, a travelling fire moves from one
burning area to the next so that the total burning duration across the floor plate is
extended. This means that there is a longer total burning duration for fires with
smaller burning areas.
As noted above, the TFM splits the temperature field into two portions: the near
field (flaming region) and the far field (hot gases away from the fire). In the case of
the 100% burning area, all of the structure will experience near field (flame)
conditions for the total burning duration (which is equal to the burning time, "#).
However, for the travelling fire cases, any one structural element will feel far field
(smoke) conditions for the majority of the total burning duration and near field
conditions for the burning time when the fire is local to the element. Therefore the
TFM must quantify both the near field and far field temperatures.
The TFM assumes the near field is 1200°C to represent worst case conditions, as this
is the upper bound of flame temperatures generally observed in compartment fires
[5]. To calculate the far field temperatures in the TFM, an engineering tool must be
selected and applied to each member of the family of fires developed. The TFM is
modular in this aspect, as any calculation method that takes fire size and geometry
as inputs and produces temperature as a function of distance from the fire may be
used.
58
As stated above, the early work [39] used a CFD fire model to study the temperature
field as a function of distance from the fire. As the case study for that work involved
an atrium, a detailed three-dimensional model was needed. Indicative results from
the case study are shown in Figure 3.6.
(a) (b)
Figure 3.6: (a) Use of CFD with the TFM in a case study with an atrium; (b) Calculated far
field temperatures for the same case study [39].
Later variations of the TFM [38, 40, 41, 42] focused on a simpler method to obtain far
field temperatures by using a ceiling jet correlation developed by Alpert [45]. This
correlation is given below in Eq. (3.3).
%�& − ∞ = 5.38�� )⁄ �+ ,⁄-
(3.3)
where %�& is the maximum ceiling jet temperature (°C)
. is the ambient temperature (°C)
) is the distance from the centre of the fire (m)
- is the floor to ceiling height (m)
0
300
600
900
1200
-25 -15 -5 5 15 25Distance [m]
Temperature at Ceiling Height [C]]
59
Note that while Alpert gives a piecewise equation for maximum ceiling jet
temperatures to describe the near field (r/H ≤ 0.18) and far field (r/H > 0.18)
temperatures, only the far field equation is used as the near field temperature is
assumed to be the flame temperature in the TFM. Although it was acknowledged
that the ceiling jet correlation does not fully characterise the fire dynamics of the
scenarios selected, it provided sufficiently accurate results to progress the
development of the TFM.
In order to limit the amount of information passed to the structural analysis, the first
iteration of the TFM by Rein et al. [39] only took a single far field temperature from
a point away from the flaming region (see red lines showing indicative temperature
in Figure 3.6b). Later versions used a fourth power average of temperature for the
far field in a bias towards radiative heat transfer [40, 41, 42]. However, in more
recent work by Stern-Gottfried et al. [38], this assumption has been relaxed and a
spatially resolved temperature field that varies with distance from the fire is used.
Instead of the average, the compartment is divided into discreet nodes, each with
their own temperature. Figure 3.7 shows representative temperature-time curves
developed at a single point for averaged and spatially resolved far field
temperatures.
The TFM provides results of the full temperature field evolution over time, which
can be used to examine particular structural elements or full frame behaviour. The
fire travels at a velocity related to its size. These velocities vary from centimetres per
minute for small fires to metres per minute for large fires, which is a broader range
than that used by Clifton in the LFM. The range of fire sizes examined in the TFM is
deemed to cover the full extent of what is physically possible in an enclosure fire.
60
Figure 3.7: Temperature-time curves at a single location in the TFM, showing averaged and
resolved far field temperatures.
In the TFM when averaged far fields are used they can be plotted together and
compared to examples of traditional methods. This is shown in Figure 3.8.
It can be seen from the results of the TFM that hotter far field temperatures last for
less time than cooler ones. The standard and parametric temperature-time curves
give similar temperatures to those in the far field from travelling fires of sizes
between 25% and 50% but do not account for the near field conditions like the TFM
does. The results of the standard fire curve cannot be explained after one hour of
burning in terms of the possible fire dynamics in.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200
Tem
pe
ratu
re (o
C)
Time (min)
Averaged
Resolved
61
Figure 3.8: Averaged far field temperatures for a family of fires in the TFM and traditional
methods as applied to a generic concrete frame 42m x 28m x 3.6m per floor [42].
While a simple plot cannot be shown for a resolved far field, the results can
nevertheless be used for heat transfer and structural analysis. Their results are better
compared to the traditional methods via the resulting structural performance, as
shown in Figure 3.9, which compares rebar heating from exposure to a 10%
travelling fire, the standard fire and two different Eurocode parametric
temperature-time curves.
The temperature fields generated from the TFM have been applied to both concrete
and steel structures by means of heat transfer analyses [38, 41]. These analyses have
looked at the temperature of either steel rebar within concrete or steel beams as a
loose surrogate for structural performance. The results showed that travelling fires
have a significant impact on the performance the structures examined and that
conventional design approaches cannot automatically be assumed to be
conservative. Medium sized fires between 10% and 25% of the floor area were found
to be the most onerous for the structure. This is due to a balance of burning duration
and far field temperatures.
0
200
400
600
800
1000
1200
1400
0.1 1 10 100
Far
Fie
ld T
em
pe
ratu
re (°
C)
Time (hours)
1%
2.5%
5%
10%
25%
50%
100%
Std Fire
EC1 25%
EC1 100%
62
Figure 3.9: Comparison of rebar temperatures calculated using a 10% fire size from the
TFM, the standard fire, and two Eurocode parametric temperature-time curves
in a similar generic concrete frame as shown in Figure 3.8 [38].
Detailed sensitivity analyses of the input parameters of the TFM have also been
conducted [38, 42], showing that the structural design and fuel load have a larger
impact on structural behaviour than any numerical or physical parameter used in
the methodology.
3.5 Structural Response
In his plenary lecture at the IAFSS Symposium in 2008, Buchanan [20] stated:
The two disciplines of combustion science and structural engineering are miles apart,
so two groups of experts will always be needed. For this reason it would be very foolish
to rush towards coupling of fire models with structural models. Any such coupling
would lead to a “black box” mentality with a major decrease in our ability to make
accurate predictions of structural fire behaviour.
0
100
200
300
400
500
600
700
800
0 50 100 150 200 250
Ba
y T
em
pe
ratu
re (o
C)
Time (min)
10% Travelling Fire
EC - 25% Ventilation
EC - 100% Ventilation
Standard Fire
10% travelling fire
equivalent to 106 min
Standard Fire
106 min
556oC
56 min38 min
363oC
252oC
63
Fire engineers and structural engineers need to talk to each other much more than
they do now, and each group needs to learn as much as possible of the other discipline.
These two topics are too big and too different for us to educate combined specialists in
both disciplines.
The comments made by Buchanan, and reinforced by Law et al. [21] highlight the
need for close collaboration between the two disciplines. The TFM has been
developed with such collaboration in mind [38, 39, 40, 41, 42].
This section reviews research involving detailed structural analysis of travelling
fires.
3.5.1 Steel Frame
The first detailed analysis of structural behaviour in response to travelling fires was
conducted by Bailey et al. [46]. This work, which was notably conducted prior to
publication of Clifton’s LFM and twelve years before Buchanan’s call for multi-
disciplinary collaboration, was pioneering in its recognition for the need to consider
the structural impact of a more realistic fire environment than the conventional
methods by examining travelling fires.
Bailey et al. extended use of a Finite Element Model (FEM) from previous research
involving uniform fires to study a two-dimensional frame exposed to a spreading
fire. The work began with a focus on the effect of the cooling phase of a fire on the
structure. The authors then note that incorporating the cooling phase allows
consideration of “fires which spread progressively from an ignition point in a single
compartment (or a zone within an open-plan area) to adjacent areas of the
building”. They go on to state:
The effect of a spreading fire is that both cooling and heating are taking place
simultaneously in different zones. This is arguably a more typical condition than the
assumption that the temperature changes uniformly throughout the fire-affected zone,
and in view of the effects of restraint observed during cooling is one which requires
investigation.
64
The study compares the response of a two-dimensional bare steel frame exposed to
a spreading fire with that of a uniform fire, over both three and five structural bays.
The uniform fire was defined by a temperature-time curve representing a “natural”
fire. The travelling fire was represented by the same natural fire curve, but offset in
time for the bays of secondary fire involvement. Once the temperature-time curve in
the first bay reached its peak, the fire was assumed to begin in the adjacent bays.
Similarly, the bays of tertiary fire involvement were assumed to ignite when the
temperature-time curve reached its peak in the secondary bays. The temperature-
time curves used are shown in Figure 3.10.
Figure 3.10: Temperature-time curves used by Bailey et al. (adapted from [46]).
While this method replicates the movement of the near field associated with
travelling fires, the use of a temperature-time curve reproduced with a delay does
not capture the far field of a travelling fire, as can be seen by the relevant details
discussed in Sections 3.3 and 3.4 of this paper. The temperature-time curve used
assumes a ventilation controlled fire. However, a fire burning in only one bay of a
structure nine bays wide is unlikely to be ventilation limited, especially in the early
0
100
200
300
400
500
600
700
800
0 50 100 150 200 250 300
Tem
pe
ratu
re (o
C)
Time (min)
First Bay
Second Bay
Third Bay
65
durations of the fire, as the air available from the rest of the structure may provide
sufficient oxygen to keep it well ventilated. Additionally, local exposure to flame
temperatures (near field conditions), and not just compartment average
temperatures associated with the calculation methods of ventilation limited fires,
are likely.
Furthermore, this method does not account for elevated smoke temperatures ofg the
far field away from the fire. The temperature in a bay adjacent to the first one
exposed remains ambient until its curve begins at 36min. Given that the bays are 8m
in dimension, it is much more likely that temperatures in the adjacent bay would be
well above ambient at this time. This behaviour could be explained if each bay were
a fully enclosed, fire rated compartment that fails 36min into the fire, however this
is not the scenario described by the authors.
Bailey et al. went on to examine the vertical displacements and axial forces in the
beams of the structure. They found that higher beam displacements occur for the
spreading fire cases than the uniform ones. The authors noted that these conclusions
cannot be readily generalised and further study is required.
3.5.2 Concrete Frame
More recently, and after the publication of the LFM and TFM, two simultaneous
papers on the impact of travelling fires on concrete frames have been published.
Ellobody and Bailey [47] conducted a study of the impact of horizontally travelling
fires on a post-tensioned concrete floor. While this study utilises sophisticated
structural analysis, including a three-dimensional FEM, the fire definition is very
similar to that used by Bailey et al. [46]. Specifically, a base temperature-time curve
is applied to the first bay of heating and is shifted in time to provide the heating of
bays that become subsequently involved in the fire. In this study, the base
66
temperature-time curve was taken from Eurocode 1. Two time delays were
examined; one of 64min and another of 30min.
The structural response was viewed in terms of tendon temperatures, deflections
and axial displacements. These parameters were examined at several critical
locations over time as well as in terms of their final residual values. Ellobody and
Bailey noticed that the “change in heating/cooling scenarios between zones resulted
in cyclic deflection patterns at some locations”. They also found that the time delay
used for shifting the temperature-time curve had an impact on the structural
response and the worst case could result from a uniform heating case or a non-
uniform travelling fire. The authors recommended that engineers consider a range
of travelling fires for use in structural design to ensure the most onerous scenario is
found.
Given a very similar method for thermal definition was used in this paper as Bailey
et al. the same critiques of the that method apply; namely the inherent assumption
of a ventilation limited fire in an open space and the lack of consideration of the far
field (hot smoke away from the fire). In fact, the cyclic deflection patterns observed
by Ellobody and Bailey could be affected by the presence of elevated far field
temperatures. This is because in their analysis some elements would be exposed to
ambient gas phase conditions while others to peak temperatures, when in reality the
ambient exposure would more likely have been that of smoke temperatures on the
order of several hundred degrees Celsius.
The work of Law et al. [42], a collaborative research project between the fire
engineers Stern-Gottfried and Rein and structural engineers Law and Gillie, applied
the TFM to a generic concrete frame 42m long x 28m wide. The temperature field
was generated as explained in Section 3.4.2 and then applied to a FEM of the
concrete frame.
67
The structural modelling results were examined in terms of rebar temperature,
sagging tensile strain, hogging tensile strain, and deflections. The results for rebar
temperature showed that fire sizes between 10% and 25% of the floor area produced
the most onerous results for the structure. All of the more detailed structural metrics
showed that the 25% fire size was most challenging for the structure. In all four
metrics the travelling fires proved to be a worse case for the structure than the
Eurocode parametric temperature-time curves. A detailed sensitivity study showed
that variations in the far field definition and differing fire shapes and paths of travel
had little impact on the results.
In his PhD thesis [48], Law further examined the structural behaviour resulting from
travelling fires, using sectional and utilisation analyses. Generally he obtained
similar results, but did notice that 5% to 10% fire sizes gave the worst case results
for the structure when using a utilisation analysis of all columns. The strength of the
methods applied by Law is that data from numerous fires can be viewed
cumulatively to get a better understanding of the behaviour of each column. This is
well suited to analyse results from the TFM which produces a family of fires.
3.5.3 Vertically Travelling Fires
Noting that large, accidental fires tend to involve multiple floors, Röben et al. [49]
examined the impact of vertically travelling fires on a multi-storey structure. The
building they examined was used in previous work by the authors to understand
the effect of the cooling phase on structural performance and had a concrete core
and a steel-concrete composite floor system.
The study assumed three floors were on fire. Although Röben et al. noted that
“horizontally travelling fires would give a more realistic representation of the fire
spread through a compartment”, the authors assumed horizontally uniform fires for
their study, stating that it is “a common assumption in structural fire design”. The
heating pattern used was similar to the horizontal studies by Bailey et al. and
68
Ellobody and Bailey, i.e. the same temperature-time curve was applied to each floor
but with a time delay between floors. The heating curve used was a generalised
exponential curve given by Flint [50]. Röben et al. noted that this curve was selected
because analysis by Flint “showed it to be a better approximation for large
compartments than the more commonly used ‘natural fire’ curves given, for
example, in the Eurocodes”, however no theoretical background or physical
justification of the method is given. The cooling phase was assumed to be linear
between the maximum and ambient temperatures over a period of 1400s.
Three fire scenarios were used; uniform heating on all three floors, a time delay of
500s between each floor, and a time delay of 1500s between each floor. The authors
noted that many factors influence the vertical spread rate. The values used in the
study were to roughly capture the range of eyewitness accounts of vertical flame
spread of between 6 and 30min in the Windsor Tower fire.
The results, primarily examined in terms of horizontal displacements of columns
and total axial forces of floors, showed that the vertically travelling fire with a short
time delay induced a similar structural response to that of the uniform heating case.
However, the primary difference observed was a “cyclic pattern induced in
columns” for the travelling fire. This pattern was also observed for the long delay
travelling fire, but with longer time intervals. The authors note that this cyclic
deflection pattern has not been examined before and has a significant impact on the
structure and, therefore, should be considered in design.
The observation of a cyclic pattern is similar to that of Ellobody and Bailey.
However, this finding perhaps has more relevance for vertically travelling fires
because compartment floors will likely limit the spread of hot gases that may
preheat the upper floors prior to full fire involvement. Notwithstanding this
argument, the nature of the column deflections may be affected by consideration of
69
horizontally travelling fires as well. However, no studies to date have examined
this.
3.6 Practical Applications
The work highlighted so far in this paper have pioneered or developed the concept
of travelling fires and the subsequent structural analyses, which is a research topic
that is beginning to grow within the fire engineering community. This section
reviews recent applications of travelling fires to real building projects found in the
literature.
The first version of the TFM has been applied to case studies in the two real
buildings. These case studies are described below.
In 2009 Stern-Gottfried et al. [40] applied the TFM to the Mumbai C70 building
project, shown in Figure 3.11a, during its early design stages. The building had 13
storeys and was approximately 60m tall. It had a unique structure, including an
external diagrid megaframe consisting of hollow structural steel members designed
to carry wind loads and a proportion of the gravity load, an internal reinforced
concrete core system designed to carry gravity load, and a hat truss at the top of the
building. The exact shape of each floor varied, with most being over 2000m2 in area.
Much of the external façade was glazed, thus placing the building outside the range
of applicability of the traditional design methods.
The 9th floor of the Mumbai C70 building was selected for structural fire analysis, as
this floor had the longest beam spans as well as slender diagrid members compared
to those found lower in the building. Therefore this floor was deemed to be where a
severe fire would be most challenging to the structure and therefore the location
studied. The first version of the TFM was used to generate temperature-time curves,
utilising an averaged far field temperature, specific for the 9th floor. The far field
70
temperatures plotted against total burning duration for a range of fire sizes for this
study are given in Figure 3.11b, with comparison to the temperature-time curves
from the standard fire and two Eurocode parametric cases.
(a)
(b)
Figure 3.11: (a) Architectural image of Mumbai C70 by James Law Cybertecture; (b) Far
field temperatures vs. total burning durations for different fire sizes, with the
standard temperature-time curve and two parametric Eurocode curves for
reference [40].
0
200
400
600
800
1000
1200
1400
0.1 1 10 100
Far
Fie
ld T
em
pe
ratu
re (°C
)
Time (hours)
1%
2.5%
5%
10%
25%
50%
100%
Std Fire
EC1 25%
EC1 100%
71
In 2010 Jonsdottir et al. [41] calculated the resultant steel temperatures from a
thermal field generated by the TFM for the Informatics Forum at The University of
Edinburgh, shown in Figure 3.12a. The Informatics Forum was completed and
occupied in 2008. The building was chosen for the study because of its unique
architectural features. It is a seven storey office building for lecturers, staff and
researchers, with a central glass atrium, and a floor area of approximately 1700m2.
The case study examined structural heating of three different steel beams based on
the temperature–time curves of the family of fires generated from the TFM. Example
results of this analysis are given in Figure 3.12b. This paper was the first to report
the resultant structural temperatures caused by travelling fires. These results were
then compared to calculations of the steel beam temperatures utilising the
traditional methods. It was found that the TFM method resulted in 10% to 55%
higher peak steel beam temperatures than the traditional methods for medium sized
fires of 10% to 25% area.
Apart from the LFM and TFM, other researchers have applied similar ideas related
to travelling fires. Sandström et al. [51] developed a pre-processing tool to rapidly
apply travelling fires as input to a CFD model (FDS v5.5). They examined a 20m x
40m x 10m, open plan building with natural ventilation in the roof and on all four
sides. They developed a design fire based on Eurocode 1 [14] guidance, which
ramps up at a “medium” t2 rate, to a peak of 95MW, then linearly decays. This
design fire was then applied using different heat release rates per unit area to define
different fire scenarios, some of which were stationary (covering 12.5% and 100% of
the floor area) and others that were travelling (using fire sizes of 0.125%, 0.5% and
2% of the floor area). It is not clear how the travelling fires were implemented and
no descriptions of the travelling nature, velocity, or burnout characteristics of the
fires were given.
72
(a)
(b)
Figure 3.12: (a) Informatics Forum at The University of Edinburgh; (b) Resultant steel
temperatures vs. time for three different beam types that were both unprotected
and fire rated to 120min [41].
The results were reported as average smoke layer temperature-time curves,
including comparison to simulations using the two-zone model OZone [18], thus
averaging the near and far fields together into a single temperature. Because of this,
0
100
200
300
400
500
600
700
800
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Ste
el T
em
pe
ratu
re (
oC
)
Time (hours)
HE-A 600
HE-A 600 120 min prot.
HE-A 300
HE-A 300 120 min prot.
HE-A 200
HE-A 200 120 min prot.
73
the analysis more closely resembles the traditional design methods that assume
homogeneous temperature conditions than the travelling fire methods already cited.
In 2010, Shestopal et al. [52] provided a review of two case studies where travelling
fires were implemented with CFD (FDS v5). The authors stated that the worst case
scenarios resulted from a spreading fire, which they used to justify the reduction of
fire resistance levels against those nominally required by the local building code.
The case studies presented were for a supermarket and an office building. In the
supermarket case study, the travelling nature of the fire was modelled via flame
spread predictions within the CFD model. In the office case study it was represented
by user specified sequential ignition along the floor (with time delays ranging from
45 to 90s) set to match experimental heat release rate data.
From the limited information presented, it appears the analyses for the supermarket
may have extended beyond the capabilities of current CFD models, by predicting
flame spread which is a challenging physical process to accurately model [25].
However, the spirit of this work, which examined spatially varying far field
temperatures, is in line with the ethos of the travelling fires methods.
3.7 Conclusions
The concept of travelling fires suggests a paradigm shift in structural fire
engineering. The dynamics of travelling fires are central to better understanding the
true structural performance of buildings exposed to real fires, and therefore the
potential to enable architectural innovation and structural optimisation.
However, given the importance of travelling fires, there has been only a limited
amount of research to date on the topic and more is needed. The earliest research by
Clifton and Bailey et al. in 1996 established the need for robust methods to account
for travelling fires. The development of the TFM in 2006 offers such an engineering
74
technique. However, refinements to the TFM for horizontally travelling fires are
needed to make it more robust. Additionally, fundamental work is needed to
examine vertically travelling fires. As opposed to horizontally travelling fires, no
framework exists to explore the dynamics of vertically travelling fires, which is
currently hindering their application in structural analysis, despite the numerous
incidents of vertically travelling accidental fires.
Of particular importance in the development and application of travelling fire
methodologies is the close collaboration between fire engineers to define to the
thermal environment and structural engineers to determine the subsequent
structural behaviour.
References
1 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance
testing – Part II”. Fire Technology, 14(4), pp. 304-316, 1978.
2 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:
Method for Determination of the Fire Resistance of Elements of Construction:
BSI, 1987.
3 ISO 834-1. Fire-resistance tests — Elements of building construction — Part 1:
General requirements.
4 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings
Construction and Materials, 2000.
5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.
6 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.
7 Manzello, S. L., Grosshandler, W. L., Mizukami, T., “Furnace Testing of Full-
Scale Gypsum Steel Stud Non-Load Bearing Wall Assemblies: Results of Multi-
Laboratory Testing in Canada, Japan and USA”, Fire Technology, Vol. 46, 2010,
pp. 191-197.
75
8 Thomas. P.H., “Modelling of compartment fires,” Fire Safety Journal, Vol. 5, 1983,
pp. 181 – 190.
9 Karlsson, B. and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.
10 Magnusson, S.E. and Thelandersson, S., “Temperature-time curves for the
complete process of fire development — a theoretical study of wood fuels in
enclosed spaces”, Acta Polytechnica Scandinavica, Stockholm, Vol. Ci 65, 1970.
11 Babrauskas, V. and Williamson, R.B., “Post-flashover compartment fires: Basis
of a theoretical model”, Fire and Materials, Vol. 2, 1978, pp. 39–53.
12 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel
Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,
1976.
13 Wickström, U., “Temperature calculation of insulated steel columns exposed to
natural fire”, Fire Safety Journal, Vol. 4, 1981, pp. 219-225.
14 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on
structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.
15 Lie, T.T., “Characteristic temperature curves for various fire severities”, Fire
Technology, Vol. 10, 1974, pp. 315-326.
16 Ma, Z. and Mäkeläinen, P., “Parametric temperature time curves of medium
compartment fires for structural design”, Fire Safety Journal, Vol. 34, 2000,
pp. 361-375.
17 Barnett, C.R., “BFD curve: a new empirical model for fire compartment
temperatures”, Fire Safety Journal, Vol. 37, 2002, pp. 437-463.
18 Franssen, J.M., “The Design Fire Tool OZone V2.0-Theoretical Description and
Validation on Experimental Fire Tests”, Civil and Structural Engineering
Department, University of Liege, Belgium, 2000.
19 Jeffers, A.E. and Sotelino, E.D., “Evaluating the Local Fire Response of Steel
Beams by Comparison to Fire Tests”, The 12th International Interflam Conference.
Nottingham, UK, 2010.
76
20 Buchanan A., “The Challenges of Predicting Structural Performance in Fires”,
The 9th International Symposium on Fire Safety Science. Karlsruhe, Germany, 2008.
21 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and
Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th
International Symposium on Fire Safety Science, University of Maryland, USA,
2011.
22 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.
14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204
23 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of
the homogeneous temperature assumption in post-flashover compartment
fires”. Fire Safety Journal, 45, 2010, pp. 249-261.
http://www.era.lib.ed.ac.uk/handle/1842/3866
24 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern
Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra
Incêndio, Natal, Brazil, 2011.
25 Rein, G., Abecassis-Empis, G., and Carvel, R. Eds., The Dalmarnock Fire Tests:
Experiments and Modelling. School of Engineering and Electronics, University of
Edinburgh, 2007.
26 Lennon, T. and Moore, D., “The natural fire safety concept - full-scale tests at
Cardington”. Fire Safety Journal, Vol. 38, 2003, pp. 623 – 643.
27 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,
“Natural Fires in Large Scale Compartments”, British Steel, 1994.
28 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation
Openings – Comparison of Long and Wide Enclosures”. The 6th International
Symposium on Fire Safety Science, Poitiers, France, 1999.
29 Thomas, I., Moinuddin, K., and Bennetts, I., “Fire development in a deep
enclosure”. The 8th International Symposium on Fire Safety Science, Beijing, China,
2005.
77
30 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,
Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the
World Trade Center Towers. NIST NCSTAR 1-5, 2005.
31 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,
Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire
Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST
NCSTAR 1-9, 2008.
32 Fletcher, I.A., Tall concrete buildings subject to vertically moving fires: A case study
approach. PhD thesis, School of Engineering, The University of Edinburgh, 2006.
http://www.era.lib.ed.ac.uk/handle/1842/3199
33 Zannoni, M. et al., “Brand bij Bouwkunde”, COT Instituut voor Veilingheids –
en Crisismanagement, December 2008.
34 Routley, J.G., “Interstate Bank Building Fire, Los Angeles, California”, U.S. Fire
Administration Technical Report 022.
35 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One
Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration
Technical Report 049.
36 Clifton, G.C., “Fire Models for Large Firecells”, HERA Report R4-83, 1996, with
proposed changes in HERA Steel Design and Construction Bulletin Issue No 54,
February 2000 and updates to referenced documents, September 2008.
37 Moss, P.J. and Clifton, G.C., “Modelling of the Cardington LBTF Steel Frame
Building Fire Tests”, 2nd International Workshop on Structures in Fire,
Christchurch, New Zealand, 2002.
38 Stern-Gottfried, J., Chapter 5 in: Travelling Fires for Structural Design, PhD Thesis,
School of Engineering, University of Edinburgh, 2011.
39 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and
Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th
International Interflam Conference, London, UK, 2007.
http://www.era.lib.ed.ac.uk/handle/1842/1980
78
40 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach
to design fires for structural analysis of non-conventional buildings: A case
study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,
http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf
41 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel
Temperatures using Travelling Fires and Traditional Methods: Case Study for
the Informatics Forum Building”. The 12th International Interflam Conference.
Nottingham, UK, 2010.
42 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling
fires on a concrete frame”, Engineering Structures, Vol. 33, 2011, pp. 1635-1642.
doi:10.1016/j.engstruct.2011.01.034. Open access version at:
http://www.era.lib.ed.ac.uk/handle/1842/4907
43 Walton, W.D. and Thomas, P.H., "Estimating Temperatures in Compartment
Fires", Chapter 3-6 of the SFPE Handbook of Fire Protection Engineering, 3rd Edition,
2002.
44 Harmathy, T.Z., “A New Look at Compartment Fires, Part II”, Fire Technology,
Vol. 8, 1972, pp.326-351, doi:10.1007/BF02590537.
45 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire
Detectors”, Fire Technology, Vol. 8, 1972, pp. 181–195.
46 Bailey, C.G., Burgess, I.W., and Plank, R.J., “Analyses of the Effects of Cooling
and Fire Spread on Steel-framed Buildings”. Fire Safety Journal, Vol. 26, 1996,
pp. 273-293.
47 Ellobody E. and Bailey, C.G., “Structural performance of a post-tensioned
concrete floor during horizontally travelling fires”. Engineering Structures, Vol.
33, 2011, pp. 1908-1917.
48 Law, A., The Assessment and Response of Concrete Structures Subject to Fire. PhD
thesis, School of Engineering, The University of Edinburgh, 2010,
http://www.era.lib.ed.ac.uk/handle/1842/4574.
79
49 Röben, C., Gillie, M., and Torero, J.L., “Structural behaviour of during a
vertically travelling fire”, Journal of Constructional Steel Research, Vol. 66, 2010,
pp. 191-197.
50 Flint, G., Fire Induced Collapse of Tall Buildings. PhD thesis, School of
Engineering, The University of Edinburgh, 2005,
http://www.era.lib.ed.ac.uk/handle/1842/1172.
51 Sandström, J., Cheng, X., Veljkovic, M., Wickström, U., and Heistermann, T.,
“Travelling Fires for CFD”, The 10th International Symposium on Fire Safety
Science, University of Maryland, USA, 2011.
52 Shestopal, V., Foley, M., Hewitt, J., Yii, E., and Bakker, F., “Spreading Fires in
FDS5 Modelling (Case Studies)” A Poster at The 12th International Interflam
Conference. Nottingham, UK, 2010.
80
81
4 The Influence of Travelling
Fires on a Concrete Frame
4.1 Introduction
Since the early 20th century, the Standard Fire test and associated temperature-time
curve [1, 2] have been used world-wide to give fire ratings to structural assemblies
and to design complete structures [3]. The Standard Fire temperature-time curve
was created in an attempt to regulate testing between different laboratories thereby
ensuring a uniform standard of safety. However, almost as soon as it was conceived,
a number of problems were identified with it. Notably, no account is taken of
differences in fuel load, fire compartment size or ventilation conditions, all of which
profoundly affect the behaviour of a compartment fire. To address some of these
shortcomings, other temperature-time curves have been proposed. Perhaps the most
widely known in structural design are the “parametric” fires curves. Initially
developed by Pettersson [4], these curves have been modified and are incorporated
82
into the Eurocode structural design standards [5]. They allow design fires to be
calculated that, unlike the Standard Fire curve, depend on the fuel load, thermal
inertia of linings, and ventilation conditions of a fire compartment. Parametric fires
therefore predict more realistic temperature-time curves than the Standard Fire and
can be roughly replicated by burning wooden cribs in a small fire compartment.
Despite these benefits, parametric fires remain very crude representations of fires in
any but the simplest of compartments, as will be described in Section 4.2. Moreover,
they are unsuitable for application in the large, open-plan spaces that are a common
feature of many modern buildings. Thus, there remain significant shortcomings
amongst the traditional design methods for specifying the thermal inputs for use in
structural fire design, particularly for large compartments.
By contrast, over the past 20 – 30 years, knowledge and understanding of how
structures respond to elevated temperatures has developed rapidly and to a point
where it is now possible to include a large variety of phenomena in structural
models and to predict the response of structures subject to known temperature
loading with good accuracy [6, 7, 8]. Coupled with the recently developed
performance-based design codes [9, 10], these capabilities have given engineers the
freedom to design structures to resist high thermal loadings in innovative, efficient
ways.
Thus, while the ability to predict subsequent structural behaviour has reached an
advanced level, the thermal inputs used in structural fire design remain simplistic,
unchanged, and not representative of actual fire dynamics in large compartments.
The various limitations inherent in the traditional design methods mean that it is
difficult to justify continuing to develop and use complex structural models when
one of the dominating input parameters – thermal loading – remains very crudely
defined. Without some development of the method for specifying design fires, it
will be impossible to obtain the “consistent level of crudeness” which has been
identified as a need within the discipline [11]. In an attempt to rectify the mismatch
83
in the levels of sophistication that are currently used for design fires and the
subsequent structural analysis, this paper adopts a new approach [12, 13, 14]. First, a
method of defining design fires that are sufficiently flexible to be applied to any fire
compartment is presented and discussed. The method has the key benefits of not
assuming a uniform temperature within a large fire compartment and allowing for
fires that travel within a compartment. Second, the paper considers the implications
of using these new design fires by applying them to the analysis of a concrete
framed structure subject to full-floor fires and comparing the predictions of various
measures of “structural distress” with those obtained when traditional fire curves
are used.
4.2 Limitations of Current Design Fires
Parametric and Standard Fires were validated by test data from small fire
compartments that were almost cubic. This test geometry allows for good mixing of
the fire gases and so is more likely to produce uniform temperature field within a
compartment. These conditions do not exist in real fires [15] and consequently
limitations must be placed on the form of compartment in which the traditional fire
curves may be used. For example, Eurocode 1 states that the parametric curves are
only valid for compartments with floor areas up to 500m2 and heights up to 4m, the
enclosure must also have no openings through the ceiling, and the compartment
linings are restricted to having a thermal inertia between 1000 and 2200J/m2s½K,
which means that highly conductive linings such as glass façades and highly
insulating materials cannot be taken into account. As a result, common features in
modern construction like large enclosures, high ceilings, atria, large open spaces,
multiple floors connected by voids, and glass façades are excluded from the range of
applicability of the current methodologies.
A recent survey of buildings in Edinburgh, UK [16], underlines the implications of
these limitations on the applicability of design fires, particularly for modern
84
structures. For buildings built over a long period of time starting in the early 20th
century, 66% of their total volume falls within the limitations. However, in a newly
constructed, modern building that has open spaces and glass façades, only 8% of the
total volume is within the limitations. This suggests that modern building design is
increasingly producing buildings that contain compartments to which parametric
fires should not be applied.
Additionally, an assumption that has remained unquestioned with each
temperature-time curve no matter how they have been applied has been that of
uniform burning and uniform compartment temperature. It is assumed that every
part of a structural element or compartment is uniformly subject to the same
temperature – as defined by the temperature-time curve adopted. Although it may
be possible to replicate these conditions in a furnace, a recent experimental review
of post-flashover tests [15] has clearly demonstrated that temperature conditions are
non-uniform in most compartments. Moreover, major fires at the Windsor Tower
[17], World Trade Center [18, 19] and TU Delft [20] have shown that fires tend to
travel around large compartments rather than burn uniformly. Tests have also
shown the there is a high degree of temperature variation even within small
compartments [21, 22, 23].
Therefore, at present, designers are forced to either use parametric fires in
compartments for which they are not strictly applicable, apply unrealistic Standard
Fires to large compartments, or to resort to CFD models of fires in large
compartments that are labour intensive to produce. There is a clear need, then, to
address the limitations of the currently available design fires if modern
performance-based design is not to be restricted.
85
4.3 Travelling Fires
In light of the various limitations outlined above, a new method for estimating
compartment fire temperatures based on the fundamental fire dynamics of the
compartment has been proposed [12, 23, 24]. This new method will be used
throughout this paper. It uses two temperature fields to represent the gas
temperature in a compartment: a high temperature in the flaming region of the fire
(the near field); and a cooler temperature for the rest of the compartment (the far
field). This approach provides a flexible technique whereby a large range of possible
fires in any compartment can be represented. For example, a fire which engulfs an
entire large floor plate simultaneously, as in traditional design methods, can be
represented, as well as a small fire that travels slowly from one end of a
compartment to the other. The full range can then be explored by parametrically
varying the size of the fire. This avoids the weakness of previous methods assuming
that arbitrary events lead to particular fire conditions, such as assuming that glazing
failure leads to one single temperature-time definition for an entire region. Instead,
consideration of a wide range of possible fire sizes covers for the inherent variable
nature of real fire events (outcome of the combination of a particular ignition
location, fuel distribution and ventilation conditions). Thus, a family of fires is
created ranging from a small travelling fire that burns for a long duration as it
travels, to a fire uniformly burning over the full extent of the floor for a shorter time
period. Therefore, the method addresses the two key shortcomings of existing
methods – restrictions on the nature of applicable fire compartments and the
assumption of uniform gas temperatures within a compartment – while still being
sufficiently concise for use in structural design.
4.3.1 Temperature Definition
The new design approach represents the horizontal temperature distribution of a
fire compartment by means of near field and far field regions, as illustrated in
Figure 4.1.
86
(a) (b)
Figure 4.1: (a) Illustration of a travelling fire; (b) Near field and far field exposure
durations at an arbitrary point within the fire compartment.
The near field is the flaming region of the fire. Peak values in small fires have been
measured in the range of 800 to 1000°C [25] but temperatures of 1200°C have been
measured for larger enclosure fires [5]. This maximum value of 1200°C is chosen for
the near field to represent the worst case conditions. The far field represents the
temperature of the hot gases away from the flaming region. Far field temperatures
can be calculated using any engineering tool that gives temperature distributions
away from the fire, including hand calculations or computer modelling. For this
study, the simple ceiling jet correlation developed by Alpert has been used [26] and
is given in Eq. (4.1).
%�& − ∞ = 5.38�� )⁄ �+ ,⁄- (4.1)
where %�& is the maximum ceiling jet temperature(°C)
∞ is the ambient temperature (°C)
� is the heat release rate (kW)
) is the distance from the centre of the fire (m)
- is the floor to ceiling height (m)
Far field (Tff) Near field (Tnf)
Near field
travels over
time
Tnf
Tff
Initial
far field
heating
Posterior
far field
heating
T∞
Near field
heating
Gas
Te
mp
era
ture
After fire
cooling
time
87
This correlation was developed for a stationary fire during steady state conditions
but is valid for travelling fires because the flame spread rate (~0.01m/s [5]) is much
lower than the velocity of the smoke (~1m/s). Thus, the far-field temperature
distribution in Eq. (4.1) moves with the fire in a quasi steady state form.
As the fire consumes the available fuel and ignites new material in its path, it moves
around the floor-plate. Consequently, the gas temperature adjacent to any given
structural element is constantly changing as the fire travels both near that element
and remote from it. To make the amount of information passed to a structural
analysis managable, the monotonically decreasing far field temperature distribution
from Alpert’s correlation is reduced to a single characteristic value, ��. To do this,
the far field temperature is taken as the fourth-power average of %�& (to favour
high temperatures in a bias towards radiation heat transfer and onerous structural
conditions) over the distance between the end of the near field, )/�, and the end of
the far field, )��. This average is calculated by Eq. (4.2).
�� = 01 2%�&345)677687 9: 4;
�)�� − )/��: 4; (4.2)
Figure 4.1 illustrates the concept of a near field and a far field for a travelling fire.
Any given location is exposed to the far field temperature for a period before the
arrival of the flaming, near field region. After all the fuel at the location has been
consumed and the near field moves away, it is then subjected to the far field
temperature again until all the fuel in the entire compartment has been consumed,
at which point the temperature returns to ambient and the structure cools.
4.3.2 Fire Size
The flexibility of the method stems from parametrically varying the size, shape, and
path of the fire. It is assumed that, once alight, any area of the floor plate will
88
continue to burn at the same rate until all the fuel is consumed. The local burning
time for any fire size can, therefore, be simply calculated from the fuel load and the
heat release rate. Once the local fuel is burnt out, the fire will move to a new area.
After the fire has travelled around the whole compartment, the cooling of the
structure takes place. The fire size is varied, in this study from 1% to 100% of the
compartment floor area. Assumptions and details of how to calculate the resultant
heating from this method can be found in other papers by the authors [13, 14, 23].
4.4 Structural Failure Criteria
The methodology presented above can be used to study the impact of different
travelling fires on the response of a structure. However, without a means to
compare the structural response, it is impossible to draw any conclusions. There are
many different methods of assessment available for fire-affected structures of
varying degrees of complexity.
The simplest and most widely used measure of structural distress is maximum
deflection. Typically, failure is defined as a ratio of deflection, e.g. span/20 [2]. The
allowable deflection does not represent a value at which an assembly
catastrophically loses stability; rather, it is the maximum deflection allowable in a
furnace test in order to protect expensive experimental equipment. In spite of this,
deflection is a simple and useful measure which can be used to give some indication
of structural distress. It is possible to use the relative deflections caused by different
fires as a means for comparison.
Another simple measure of performance for concrete structures is the maximum
temperature of the tension reinforcement. Failure in steel members is often said to
have occurred when the axial capacity of a section is half its ambient capacity. For
reinforcing steel in concrete, this critical temperature is typically taken as 593°C [27].
Again, although this is a fairly arbitrary measure of “failure”, the temperature of the
89
rebar offers a simple and easily comparable metric that can be used to examine the
relative impact of different fires on a structure.
The ultimate strain in the tension reinforcement is also often used as a definition of
failure; beyond this strain, the rebar can be assumed to have failed. This measure is
better suited to the numerical analysis of structures than to fire tests because of the
difficulties associated with instrumentation of rebar. However, the strain in the
tension steel provides another measure which can be used to compare the relative
impact of the different fires. The ultimate strain for steel at any temperature is
typically taken as 0.2 [10, 28].
4.5 Structural Modelling
The remainder of this paper is a case study that demonstrates how the above
travelling fire methodology and failure measures can be applied in a structural
analysis. Initially, a number of base case scenarios are considered and the
differences between the predicted structural responses compared; a parametric
study is then conducted to assess the validity and effect of the various assumptions
made by the new approach. Finally, the impact of the shape and path of the fire is
considered.
4.5.1 Structural Arrangement
The case study analyses the impact of travelling fires on a generic concrete office
building. The structure is a nine storey, flat-slab concrete frame, designed in
accordance with the Eurocodes [29, 30, 31]. A plan and elevation of the structure are
shown in Figure 4.2. The floor slabs are 200mm thick; the interior columns
400mm x 400mm; and the exterior columns 300mm x 300mm. The design strength of
the concrete in the columns is 48MPa, and that in the slabs 40MPa. In this paper fires
burning on the fourth floor are considered. This allows the structural effects of a
90
mid-level fire to be analysed without the need to explicitly consider effects of the
foundations or the building’s top storey.
Figure 4.2: Plan and elevation of concrete structure, dimensions in metres.
Two finite-element models of the central floors of the structure were created using
the commercially available Abaqus [32] software. One was a heat-transfer model
developed to determine structural temperatures, the other a stress analysis model
produced to predict the mechanical response of the structure. The models were
sequentially coupled so the heat-transfer analysis results affected the mechanical
response. Both models extended from the base of the columns at the third-storey
level, to the top of the columns at the fifth-storey level. The floor slabs were
modelled using shell elements, the columns using three-dimensional solid elements
and the rebar using truss elements.
In the heat-transfer model, thermal properties were specified in accordance with
those of a 1.5% moisture content concrete, as defined in Eurocode 2 [9]. Heating of
the structure was analysed by applying relevant radiative and convective boundary
conditions to the surface of the structure. For the purposes of this study, an
91
emissivity of 0.7 and a convective coefficient of 25W/m2K were assumed in
accordance with Eurocode guidance [9].
For the mechanical analysis, all of the material properties used in the model were
temperature dependent and in accordance with Eurocode 2 and the yield criterion
used for the concrete was the “damaged plasticity” model, based on the work of
Lubliner [33]. A series of mesh sensitivity studies were conducted to find the
optimum mesh density. The final mesh density used was 8 × 8 × 18 elements per
floor per column, and an average element size of 0.4735m in the slab.
The base of each column was assumed to be fixed in translation and rotation, and
the top of each column was fixed in all directions other than vertical. As the higher
storeys of the structure were not modelled, the equivalent loads that would have
been transferred into the column heads were calculated using a full-frame elastic
model and applied to the remaining structure during the loading phase of the
analysis. The central core of the building was not modelled explicitly but was
assumed to provide rigid support to the adjoining structure.
4.6 Base Case Fires
The base case family of fires were defined as fires that travelled linearly from one
side of the structure to the other, as shown in Figure 4.3. The fire sizes considered
were: 1%, 2.5%, 5%, 10%, 25%, 50% and 100% of the floor area. It was assumed that
the fuel load, $�, was 570MJ/m2 and the heat release rate per unit, � ", was
500kW/m2. The distance to the far field for Alpert’s equation was measured from the
centre of the fire at the mid-point of the building along the direction of fire travel, as
shown in Figure 4.4. This creates the shortest far field distance, which in turns leads
to the highest far field temperature possible for that specific scenario. This is done to
err on the side of conservatism. Figure 4.4 shows the distances to the end of the near
field and to the end of the far field for both the case where the near field is smaller
92
than the core and the case where it is larger. The near field distance is simply
calculated from the geometry of the structure and the fire area for each case.
(a) (b)
Figure 4.3: (a) Progression of the 2.5% fire across the floor plate; (b) Progression of the 25%
fire across the floor plate. Bay numbers are indicated in both figures.
(a) (b)
Figure 4.4: The measurement of )�� and )/� for two different indicative fire sizes:
(a) small; and (b) large.
The fuel conditions above resulted in a local burning time of 19min for any single
area. For example, as there were four phases in the 25% fire size, it lasted for a total
burning duration of 76min, and had a far field temperature of 805°C. The near field
6
5
4
3
2
1
Far field
Far field
Near field
A
B
6
5
4
3
2
1
Far field
Far field
Near field
A
B
Near field
rnf
rff
Near field
rnf
rff
93
temperature is taken as the flame temperature, assumed to be 1200°C [13]. The 2.5%
fire size, meanwhile, had a total burning duration of 760min and a far field
temperature of 325°C. Figure 4.5 shows the total burning duration and far field
temperatures for each of the base case fires. It should be noted for the 100% fire size,
the far field temperature is the same as the near field temperature.
Figure 4.5: Far field temperatures vs. total burning durations for different fire sizes.
Standard and two (“short hot” – EC1 100% and “long cool” – EC1 25%)
parametric Eurocode fire curves are also shown for reference.
4.6.1 Structural and Thermal Analysis
Thermal and structural analyses were conducted using the finite-element model
described above. To allow meaningful conclusions to be drawn from the modelling,
it should be noted that the analyses were intended to be comparative. Therefore, for
the remainder of this paper, the metrics that will be used to quantify the response of
the structure will be the three simple measures discussed above – temperature,
strain in the tension steel, and central deflection of each bay.
0
200
400
600
800
1000
1200
1400
0.1 1 10 100
Far
Fie
ld T
em
pe
ratu
re (°
C)
Time (hours)
1%
2.5%
5%
10%
25%
50%
100%
Std Fire
EC1 25%
EC1 100%
94
Figure 4.3 shows the location of the near field part of the way through the 2.5% and
25% fire sizes. The heat transfer analyses allowed the temperature in the slab soffit
rebar to be monitored. Figure 4.6 shows the gas temperatures and corresponding
rebar temperatures for points A and B (indicated in Figure 4.3) during the 10% fire.
(a)
(b)
Figure 4.6: (a) Gas temperature and corresponding rebar temperature at point A; (b) Gas
temperature and corresponding rebar temperature at point B for a 10% linearly
travelling fire.
The influence of the near field on the rebar can be clearly seen as a temporary
increase in temperature. The prolonged exposure of point B to the far field prior to
the arrival of the near field causes the overall peak temperature to be higher than
that at point A. Figure 4.7a shows a similar plot of the temperature profiles for the
soffit rebar at the centre of bays 1 – 6 for the 5% fire size. It can be clearly seen that
the final bay to be subjected to the near field experienced the highest temperature;
the long pre-heat induced a higher maximum temperature in this bay which caused
it to be most critical by this metric. This trend was the same with each of the base
case fires.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400
Tem
pe
ratu
re (o
C)
Time (min)
Gas temperature
Rebar temperature
Point A
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400
Tem
pe
ratu
re (o
C)
Time (min)
Gas temperature
Rebar temperature
Point B
95
(a)
(b)
Figure 4.7: (a) Single point rebar temperature at the centre of bays 1 – 6 during the 5% base
case fire; (b) Average rebar temperatures for the whole of bays 1 – 6 for the 5%
base case fire.
Figure 4.7b shows the average temperature in the soffit rebar for each bay. Because
the near field of the 5% fire size does not cover the whole area of any bay
simultaneously, the average rebar temperatures are lower. The bay average rebar
temperatures are a more representative measure of structural vulnerability as they
will not be distorted by localized heating effects. For example, were a localized fire
to heat only a tiny area of the bay, it would have minimal impact on the overall
structural behaviour, but would induce high rebar temperatures. Thus, the bay
average rebar temperatures will be used as the measure of rebar temperature for the
remainder of this paper rather than point temperatures.
A comparison of the rebar temperatures induced in the final bay by the different
fires in the family is given in Figure 4.8 and shows clearly that the highest
0
100
200
300
400
500
600
0 100 200 300 400 500 600
Tem
pe
ratu
re (o
C)
Time (min)
Point 1Point 2Point 3Point 4Point 5Point 6
65432
1
0
100
200
300
400
500
0 100 200 300 400 500 600
Tem
pe
ratu
re (o
C)
Time (min)
Bay 1Bay 2Bay 3Bay 4Bay 5Bay 6
65432
1
96
temperatures are caused by the medium duration fires: 10% and 25% fire sizes. For
the 2.5% fire the arrival of the near field at bay 6 is labelled, as is the end of the fire.
Figure 4.8: Temperature profiles for the average rebar in the final bay to be heated during
the base case fires.
A similar process was conducted for each of the structural measures. The absolute
value of each measurement technique can be normalised with respect to the
appropriate failure definition: 593°C for rebar temperature, span/20 for deflection,
and 0.2 for rebar strain. It is possible therefore to observe how the level of structural
distress varies with each curve in the family of fires. Figure 4.9 shows the trends for
each of the measures against fire size. As a comparison the structure was also
subjected to a Standard Fire, a “short hot” parametric fire and a “long cool”
parametric fire. The “short hot” fire had a peak temperature of 989°C and a total fire
time of 37min, and the “long cool” fire had a peak temperature of 915°C and a total
fire time of 145min. Both curves were generated by the parametric temperature-time
from Eurocode 1 [31] for the building being examined, varying the assumed glass
breakage in the façade for the ventilation factor. The short hot fire assumed 100%
glazing failure along the façade while the long cool fire assumed 25%.
0
100
200
300
400
500
0 200 400 600 800 1000 1200
Tem
pe
ratu
re (o
C)
Time (min)
2.5% Base
5% Base
10% Base
25% Base
50% Base
100% Base
Arrival of Near Field
End of Fire
97
Figure 4.9: Change in structural distress with near field area: (top left) rebar temperature,
Standard Fire equivalent is 1h 37min; (top right) sagging tensile strain, value for
Standard Fire given after 3h; (bottom left) hogging tensile strain, Standard Fire
equivalent is 1h 18min; and (bottom right) deflection, Standard Fire equivalent
is 1h 54min.
The 25% fire size induced the highest degree of structural distress in each of the
failure metrics. The trend in every metric was the same: the medium sized fires (5%,
10% and 25%) caused a higher degree of structural distress than both the smaller
and the larger sized fires. It is also notable, that the temperature and deflection
measures show the structure as much closer to “failure” than the strain measures.
For each measure, a comparison with Standard and parametric fires is also made.
The parametric fires universally induced less extreme structural conditions than the
medium fire size base case scenario. The worst case travelling fire was equivalent to
1hr 37min of the of a Standard Fire in terms of rebar temperature, 1hr 18min for
hogging tensile stain and 1hr 54min for deflection. In contrast, the sagging strain
was less than that obtained during most of the base case and “long cool” fires; this
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 25% 50% 75% 100%
No
rma
lise
d T
em
pe
ratu
re
Fire Area
Rebar Temperature
Standard Fire
Parametric - Short Hot
Parametric - Long Cool0
0.01
0.02
0.03
0.04
0.05
0.06
0% 25% 50% 75% 100%
No
rma
lise
d S
tra
in
Fire Area
Sagging Strain
Standard Fire
Parametric - Short Hot
Parametric - Long Cool
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0% 25% 50% 75% 100%
No
rma
lise
d S
tra
in
Fire Area
Hogging Strain
Standard Fire
Parametric - Short Hot
Parametric - Long Cool0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 25% 50% 75% 100%
No
rma
lise
d D
efl
ect
ion
Fire Area
Deflection
Standard Fire
Parametric - Short Hot
Parametric - Long Cool
98
was because there was no cooling phase during the Standard Fire so the structure
was not pulled into tension.
The results of the base case fires, and their comparison with the codified fires, have
shown that the traditional design methods do not necessarily produce the most
onerous case for the structure. Indeed a travelling fire based on fundamental fire
dynamics can induce a worse structural scenario. This is in agreement with previous
work for steel structures [12, 34]. It has been shown that the medium size (and
duration) fires induce the most extreme structural response; the short large fires and
the long small fires are less severe for the structure. Specifically the 25% area fire
produced the worst case for the structure. It has also been found that the lack of a
cooling phase in the Standard Fire does not allow all the forces that are likely to
develop over the course of a real fire to develop; it cannot, therefore be considered
conservative [35].
4.7 Parametric Study
A parametric study was conducted to establish the effect of the various assumptions
made in the travelling fire methodology on the predicted structural response. As the
25% fire was found to be the most severe by every metric for this structure, this fire
size was used throughout the parametric study.
4.7.1 Far Field Definition
First, the method used to define the far field temperature was varied, and the
response of the structure was monitored using the same metrics that were used in
the previous section. The cases studied are described below and illustrated in
Figure 4.10.
1. Single far field (base case). As with the previous analyses, Alpert’s far field
temperature profile was reduced to a single value by fourth power
averaging. The progress of the fire was assumed to move suddenly, i.e. it
99
would jump from one quarter of the floor plate to the next after each burning
time. This assumption means the fire is in four specific locations (for the 25%
area fire) over the total burning duration.
2. Two far fields. Rather than reducing the far field to a single value for both
sides of the burning area, two separate far fields were assumed, one on
either side of the fire. Each far field had a unique temperature defined with
the fourth power average.
3. Alpert’s temperature profile (sudden). Rather than averaging the far field
temperature as above, the continuous temperature profile defined by
Alpert’s equation (Eq. 4.1) was directly applied to the structure. As with the
base case, the fire moved suddenly from area to area as the fuel was
consumed.
4. Alpert’s temperature profile (gradual). Alpert’s temperature profile was
used to define the far field, but the fire was assumed to progress gradually
across the structure, rather than jumping suddenly from one area to the next.
Figure 4.10: Example range of far field temperature definitions.
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35 40 45
Tem
pe
ratu
re (°
C)
Distance from End (m)
One Far Field
Two Far Fields
Resolved Far Field
100
The results in Figure 4.11 show that there is little variation in the performance
metrics between the different approaches of defining the far field temperature. As
with the data in Figure 4.9 the results for each metric are normalised against the
relevant failure definition: 593°C for rebar temperature, span/20 for deflection, and
0.2 for rebar strain. Of the different proposed profiles, the “Alpert – sudden”
induced the greatest distress in terms of deflection (0.29m, normalised value of 0.84)
and hogging tension strain (0.03, normalised value of 0.19). However, these values
were only 0.5% and 3.6% in excess of the base case value, respectively. In terms of
rebar temperature, the base case had the highest value (450°C) by a marginal
amount (0.1% higher than the “two far fields” case) and the total variation between
the largest and smallest temperature was 10.6%. The largest value in terms of the
sagging tensile strain was obtained during the “Alpert – gradual” case (0.01). For
this profile, the maximum strain measured was 4.7% larger than the base case
equivalent.
Figure 4.11: The effect of far field temperature definition on each failure metric.
This study shows that the variations induced by the different fires in the most
critical structural measures are negligible. The variation in the less distressed
measures was slightly larger, but still remained small (<5%). It therefore appears
reasonable that the use of the simple, averaged, temperature profile, i.e. the base
0
0.25
0.5
0.75
1
Base case Alpert - Gradual Alpert - Sudden Two far fields
Norm
alised Faliure Criterion
Deflection Temperature Hogging strain Sagging strain
101
case, for the whole of the far field temperature region provides appropriate results
and a higher level of detail is not needed. This makes the temperature definitions in
the heat transfer model significantly simpler to apply: a key consideration for the
use of such an approach in a design context.
4.7.2 Fire Shape and Path
The base case fire described above started at one end of the structure and then
progressed linearly across the floor-plate. A real fire could follow a number of
possible paths and it has long been recognised that to examine every possible fire
scenario would be unfeasible due to the large number of analyses required [3].
However, since the advent of modelling techniques such as the finite-element
method it has become possible to evaluate a number of different structural scenarios
quickly. This paper has developed a number of fires and applied them to the same
structure. In an attempt to quantify the impact that different fire paths and shapes
have on the structure, this study analyses the effect of three other possible fire
patterns with a fire size of 25% of the floor area. In addition to the linear base case,
the different fire shapes are illustrated in Figure 4.12 and are described below:
• Corner Fire. Initiated in one corner of the structure and spread around the
building’s core. Due to symmetry, results are the same for clockwise and
anti-clockwise fires.
• Ring Fire, Outwards. Initiated as a ring around the core, and spread
concentrically outwards.
• Ring Fire, Inwards. Initiated in a peripheral ring around the edge of the
structure, and spread concentrically inwards towards the core.
102
Figure 4.12: Illustration of different fire shapes and paths.
The results were broadly similar with some metrics showing an increase and some
showing a decrease but there is some variation between the different fires paths.
The corner fire was found to be the most severe scenario. The relative increase in
comparison to the base case model was 8% for deflection (0.32m); 5% and 10% (0.04
and 0.01) for hogging and sagging strain respectively; and no change in the rebar
temperature. Figure 4.13 shows the difference between the four fire shapes
analysed. Therefore it can be concluded that the shape and path of the fire does
have a small impact on the response of the structure.
Figure 4.13: The influence of fire shape and path on the failure metrics.
1st burn region 2nd burn region 3rd burn region 4th burn region
Base case Corner Ring - InwardsRing - Outwards
0
0.25
0.5
0.75
1
Base case Ring - Inwards Ring - Outwards Corner
Norm
alised Faliure Criterion
Deflection Temperature Hogging strain Sagging strain
103
4.8 Summary and Concluding Remarks
A comparative analysis of the impact of a number of different design fires on a
concrete frame has been conducted. A new approach to defining temperature-time
curves for design has been presented. The relative impact of the conventional
codified curves and the new travelling fire methodology has been studied.
The travelling fire approach is based on observations from real, large building fires,
and founded on the fundamental fire dynamics of a large open plan floor plate. It
allows a range of realistic fires to be considered and, thus, allows structural
engineers to better understand how different fires might affect the behaviour of a
building. Though based on complex temperature distribution data, a simplified
approach allows a single value far field temperature distribution. It has been
demonstrated that this simplification is a good approximation to more complex
temperature fields obtained from fundamental fire dynamics. The simplified far
field approach is easily implemented in finite-element codes.
The generic concrete frame which was subjected to the various fires was the same in
each of the analyses. It has thus been possible to draw strong comparative
conclusions, particularly given the variety of measures used to assess the structure,
which include:
• Travelling fires have a more severe impact on the performance of this
structure than the Eurocode parametric fires. The Eurocode fires cannot,
therefore, be considered conservative.
• The fires of medium duration and fire size are the most severe in terms of
their impact on the structure.
• The 25% fire size fire was conclusively found to be the most severe by every
measure used.
104
• The assumption of a simplified far field temperature was valid: more
complex and realistic temperature profiles had little impact on the overall
structural behaviour.
References
1 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings
Construction and Materials, 2000.
2 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:
Method for Determination of the Fire Resistance of Elements of Construction:
BSI, 1987.
3 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance
testing – Part II”. Fire Technology, Vol. 14, 1978, pp. 304-316.
4 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel
Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,
1976.
5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.
6 Franssen, J.M., Cooke, G.M.E., and Latham, D.J., “Numerical simulation of a full
scale fire test on a loaded steel framework”. Journal of Constructional Steel
Research Vol. 35, 1995, pg 377.
7 Bailey, C.G., Burgess, I.W., Plank, R.J., “Computer Simulation of a Full-Scale
Structural Fire Test”, The Structural Engineer Vol. 74, 1995, pg 93.
8 Gillie, M., Usmani, A.S., and Rotter, J.M., “A Sturctural Analysis of the
Cardington British Steel Corner Test”, Journal of Construction Steel Research”,
Vol. 58, 2002, pg. 427.
9 EN1992-1-2. Eurocode 2: Design of Concrete Structures - Part 1-2: General rules
- Structural fire design, 2004.
10 EN1993-1-2. Eurocode 3: Design of Steel Structures - Part 1-2: General rules -
Structural fire design, 2005.
105
11 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,
The 9th International Symposium for Fire Safety Science, Karlsruhe, Germany, 2008.
12 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach
to design fires for structural analysis of non-conventional buildings: A case
study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,
http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf
13 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and
Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th
International Interflam Conference, London, UK, 2007.
http://www.era.lib.ed.ac.uk/handle/1842/1980
14 Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel Guide”, Fire Risk
Management, November 2009. pp. 12-16.
15 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of
the homogeneous temperature assumption in post-flashover compartment
fires”. Fire Safety Journal, 45, 2010, pp. 249-261.
http://www.era.lib.ed.ac.uk/handle/1842/3866
16 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.
14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204
17 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based
analysis of a concrete building subjected to fire,” Advanced Research Workshop on
Fire Computer Modelling, Santander, Spain, 2007,
http://www.era.lib.ed.ac.uk/handle/1842/1988.
18 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,
Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the
World Trade Center Towers. NIST NCSTAR 1-5, 2005.
19 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,
Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire
Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST
NCSTAR 1-9, 2008.
106
20 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT
Instituut voor Veilingheids – en Crisismanagement, 2008.
21 Abecassis-Empis, C., Reszka, P., Steinhaus, T., Cowlard, A., Biteau, H., Welch,
S., Rein, G., and Torero, J.L., “Characterisation of Dalmarnock fire test one,”
Experimental Thermal and Fluid Science, Vol. 32, pp. 1334 – 1343, 2008.
22 Welch, S., Jowsey, A., Deeny, S., Morgan, R., and Torero, J.L., “BRE large
compartment fire tests–characterising post-flashover fires for model
validation”. Fire Safety Journal, vol. 42, pp. 548 – 567, 2007.
23 Stern-Gottfried, J., Law, A., Rein, G., Gillie, M., and Torero, J.L., “A Performance
Based Methodology Using Travelling Fires for Structural Analysis”, The 8th
International Conference on Performance-Based Codes and Fire Safety Design Methods.
Lund, Sweden, 2010.
24 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G. “The Influence of Travelling
Fires on the Response of a Concrete Frame”, International Conference of Structures
in Fire. Lansing, Michigan, USA, 2010.
25 Audoin, L., Kolb, G., Torero, J.L., and Most, J.M.. “Average centreline
temperatures of a buoyant pool fire obtained by image processing of video
recordings”, Fire Safety Journal, Vol. 24, 1995, pp. 167-187. doi:10.1016/0379-
7112(95)00021-K.
26 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire
Detectors”, Fire Technology, Vol. 8, 1972, pp. 181–195.
27 Kodur, V.K.R. and Harmathy, T.Z., “Properties of Building Materials”, SFPE
Handbook of Fire Protection Engineering. 2008.
28 CEB-FIB. Fire Design of Concrete Structures: Structural Behaviour and
Assessment. Lausanne: FiB, 2008.
29 EN1992-1-1. Eurocode 2: Design of Concrete Structures - Part 1-1: General rules
and rules for buildings, 1999.
30 EN1992-1-2. Design of Concrete Structures - Part1-2: General rules- Structural
fire design, 1992.
107
31 EN1991-1-2. Eurocode 1: Actions of Structures - Part 1-2: General Actions -
Actions on Structures Exposed to Fire, 1999.
32 ABAQUS. ABAQUS Analysis User's Manual. Providence: Dassault Systemes
Simulia Corp, 2008.
33 Lubliner, J., Oliver, J., Oller, S., and Onate, E., “A Plastic-Damage Model for
Concrete”, International Journal of Solids and Structures Vol. 25, 1989 pg. 299.
34 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel
Temperatures using Travelling Fires and Traditional Methods: Case Study for
the Informatics Forum Building”. The 12th International Interflam Conference.
Nottingham, UK, 2010.
35 Röben, C., The effect of cooling and non-uniform fires on structural behaviour. PhD
thesis, School of Engineering, The University of Edinburgh, 2006.
108
109
5 Refinement and
Application of the Travelling
Fires Methodology
5.1 Introduction
Close inspection of accidental fires in large, open-plan compartments reveals that
they do not burn simultaneously throughout an entire enclosure. Instead, these fires
tend to move across floor plates as flames spread, burning over a limited area at any
one time. These fires have been labelled “travelling fires”.
Despite these observations, fire scenarios currently used for the structural fire
design of modern buildings are based on one of two traditional methods for
specifying the thermal environment; the standard temperature-time curve (which
has its origins in the late 19th century [1]) or parametric temperature-time curves,
110
such as that specified in Eurocode 1 [2]. These methods assume uniform burning
and homogeneous temperature conditions throughout a compartment, regardless of
its size. These two assumptions, which have never been confirmed experimentally,
lead to limitations in the use of the traditional methods in large compartments.
Details of the limitations and their implications are given in the literature [3, 4, 5].
Accidental fires that have led to structural failure [6, 7, 8, 9] have been observed to
travel across floor plates, and vertically between floors, rather than burn uniformly.
Travelling fires have also been observed experimentally in compartments with non-
uniform ventilation [10, 11, 12].
Even though the traditional methods have inherent assumptions of fire behaviour
different from that observed in accidental and experimental fires, in the past they
were generally deemed to be conservative, and therefore appropriate for
engineering design. However, recently travelling fires have been shown to be more
challenging to structures than the design fires from traditional methods [4, 13].
Moreover, recent advances in structural analysis and modelling techniques are
aimed at determining the true performance of a building exposed to fire. Therefore,
there is a need for a more realistic definition of fire scenarios to obtain a more
accurate characterisation of building performance. Because current engineering
analysis of the structural response often involves the use of sophisticated computer
modelling, it is also important to ensure a consistent level of crudeness across the
whole analysis [14, 15].
To address this need, a methodology that utilises physically-based fire dynamics for
large enclosures, based on travelling fires, has been developed. It has been
formulated to enable collaboration between fire safety engineers to define the fire
environment and structural fire engineers to assess the subsequent structural
behaviour, which is an identified need within the structural fire community [14, 15].
111
This paper presents the general framework and analytical details of this travelling
fires methodology, which produces temperature fields for a range of fire sizes.
These results are used to calculate the heating of a generic concrete structure. A
sensitivity study is conducted to determine the relative impact of the methodology’s
numerical, physical and building parameters on the structure.
5.2 Travelling Fires Framework
The goal of the methodology developed in this paper is to calculate the fire-induced
thermal field such that it is physically-based, compatible with the subsequent
structural analysis, and accounts for the fire dynamics relevant to the specific
building being studied. In order to achieve this, a fire model must be selected that
provides the spatial and temporal evolution of the temperature field. This model is
then applied to the particular compartment of interest.
The fire-induced thermal field is divided in two regions: the near field and the far
field. These regions are relative to the fire, which travels within the compartment,
and, therefore, move with it. The near field is the burning region of the fire and
where structural elements are exposed directly to flames and experience the most
intense heating. The far field is the region remote from the flames where structural
elements are exposed to hot combustion gases (the smoke layer) but experience less
intense heating than from the flames. The near and far fields are illustrated in Figure
5.1.
Because the initiation and end of the fire results in a very fast rise and decrease in
gas temperature relative to the structural heating, these phases can be assumed to be
instantaneous for the temperature field (see Figure 5.8 for a fast return to ambient).
This is because the larger an enclosure is, the lower the importance of the thermal
inertial of its linings, thus the faster the growth and decay phases will be. In other
words, the transport of the hot gases in the smoke layer is faster than the heat
112
transfer to the surfaces. Note that the cooling of the structure is not neglected; only
the brief decay phase of the fire environment is shortened.
(a) (b)
Figure 5.1: (a) Illustration of a travelling fire; (b) Near field and far field exposure
durations at an arbitrary point within the fire compartment.
For most large compartments, travelling fires are likely to be fuel bed controlled. In
fact, a recent review by Majdalani and Torero [16] of early CIB tests and the
resulting analyses of compartment fire behaviour done by Philip Thomas and others
highlights that ventilation controlled fires are unlikely in large enclosures and that
they are not necessarily more conservative for structural analysis than fuel bed
controlled fires. Majdalani and Torero note that while the different burning
behaviour between ventilation and fuel bed controlled fires was clearly stated in the
original studies, ventilation controlled fires have nonetheless been assumed to be
the most severe case for design. Therefore traditional methods of calculating the
burning rate, based on correlations for ventilation limited fires in relatively small
compartments, are inappropriate for use with travelling fires.
The methodology does not assume a single, fixed fire scenario but rather accounts
for a whole family of possible fires, ranging from small fires travelling across the
floor plate for long durations with mostly low temperatures to large fires burning
for short durations with high temperatures. Temperature-time curves for a family of
fires are shown in Figure 5.2. Using the family of fires enables the methodology to
Far field (Tff) Near field (Tnf)
Near field
travels over
time
TimeG
as
Tem
pe
ratu
re
Near Field
Initial
Far Field
Heating
Posterior
Far Field
Heating
Post Fire
Cooling
Tnf
T∞ ttotaltb
113
overcome the fact that the exact size of an accidental fire cannot be determined a
priori. This range of fires allows identification of the most challenging heating
scenarios for the structure to be used as input to the subsequent structural analysis.
Figure 5.2: Temperature-time curves on a log x-axis for a family of fires at the final location
along the fire path. Cooling to ambient temperature starts after the last point in
each curve.
Each fire in the family burns over a specific surface area, denoted as ��, which is a
percentage of the total floor area, �, of the building, ranging from 1% to 100%.
Compared to this approach, the conventional methods only consider full size fires,
which are analogous to the 100% fire size in this methodology. All other burning
areas represent travelling fires of different sizes which are not considered in the
conventional methods.
The methodology is independent of the fire model selected and can utilise simple
analytical expressions or sophisticated numerical simulations. The first version of
this methodology used the Computational Fluid Dynamics (CFD) code Fire
0
200
400
600
800
1000
1200
1400
0.01 0.1 1 10 100
Ga
s Te
mp
era
ture
(oC
)
Time (hours)
1.25%
5%
10%
25%
50%
100%
114
Dynamics Simulator (FDS) as the fire model [17]. Later work was developed using
an analytical correlation [4, 13, 18]. The work in this paper is developed further from
the earlier analytical work of Law et al. [4]. Details of each step of the methodology
are given in the following section.
5.3 Analytical Model
The analytical correlation used, in lieu of CFD modelling, was selected for several
reasons. The analytical model is simple and easy to use, while still providing the
correct dynamics (see Section 5.3.2). It also provides a consistent level of crudeness
with the heat transfer calculations performed to assess structural performance. And
it does not have the high computational cost of CFD (which is on the order of days
to calculate one fire scenario) associated with it and, therefore, enables consideration
of many more scenarios and sensitivity studies than would have been practical with
CFD models.
It is noted, however, that the correlation used is a simplification of the actual fire
dynamics of the cases being examined and is only applicable to a limited set of
scenarios where it is valid, such as a single floor without interconnection to other
levels. However, given the benefits of the points listed above, the analytical
correlation was deemed sufficient to progress development of the methodology.
The following sections present the details needed to calculate the temperature field
for the family of fires, using the analytical correlation selected.
5.3.1 Burning Times
As the exact size of a potential fire in a building cannot be determined a priori, and
the calculation methods for burning rates are inappropriate for large compartments,
this methodology assumes the heat release rate of a fire by considering a wide range
of possible sizes. It is assumed that there is a uniform fuel load across the fire path
115
and that the fire will burn at a constant heat release per unit area typical of the
building load under study. From this, the total heat release rate is calculated by Eq.
(5.1).
� = ��� " (5.1)
where � is the total heat release of the fire (kW)
�� is the floor area of the fire (m2)
� " is the heat release rate per unit area (kW/m2)
The local burning time of the fire over area, ��, is calculated by Eq. (5.2).
"# = $�� " (5.2)
where "# is the burning time (s)
$� is the fuel load density (MJ/m2)
For the case study presented below, the fuel load density, $�, is assumed to be
570MJ/m2, as per the 80th percentile design value [19] for office buildings. The heat
release rate per unit area, � ", is taken as 500kW/m2 which is deemed to be a typical
value for densely furnished spaces, as design guidance [20] gives this value for retail
spaces. Based on these two values, the characteristic burning time, "#, is calculated
by Eq. (5.2) to be 19min. This time correlates well to the free-burning fire duration of
domestic furniture, which Walton and Thomas [21] note is about 20min. It is also in
line with Harmathy’s [22] observation that a fully developed, well ventilated fire
will normally last less than 30min.
Note that the burning time is independent of the burning area. Thus the 100%
burning area and the 1% burning area will both consume all of the fuel over the
specified area in the same time, "#. However, a travelling fire moves from one
116
burning area to the next so that the total burning duration, "EFE�G, across the floor
plate is extended (see Eq. (5.9) in Section 5.3.3). This means that there is a longer
total burning duration for smaller burning areas.
The total burning duration for a single fire size can reach a theoretical maximum,
denoted as "EFE�G∗ , which is equal to the local burning time multiplied by the ratio of
floor area to the fire size, plus one additional local burning time. For example, a 25%
fire has a ratio of floor area to fire area of four, so adding one local burning time to
this gives five times the local burning time, or 95min, for the total burning duration.
Similarly, the maximum total burning duration for a 1% fire is 1919min. For full
details of the derivation of "EFE�G∗ , see Eq. (5.10) in Section 5.3.3.
5.3.2 Near Field vs. Far Field
The near field is dominated by the presence of flames. The maximum possible
structural heating would result from direct contact of the flames and a structural
element. Hence it is assumed that there is direct contact and peak flame
temperatures are used in this methodology. These temperatures have been
measured in small fires in the range of 800 to 1000°C [23] and up to 1200°C in larger
fires [24]. The maximum value of 1200°C is chosen here for the near field
temperature to represent worst case conditions. A sensitivity study on the effect of
this parameter value over the experimental range of peak flame temperatures is
presented in Section 5.5.7.
The far field temperature decreases with distance from the fire. The maximum
exposure to hot gases results when the structural element is on the exposed side of
the ceiling. Therefore temperatures at the ceiling are used in this methodology. An
analytical expression capturing the decrease of temperature with distance as a
function of the fire heat release rate would take the general form given in Eq. (5.3).
117
��2I3 = J� KLIMN (5.3)
where �� is the far field temperature (°C)
� K is the convective heat release rate (W)
J is a constant parameter related to geometry and physical properties (-)
I is the horizontal distance from the fire (m)
O is the power law coefficient for heat release rate (-)
P is the power law coefficient for distance (-)
The decrease with distance is due to the incremental mixing of hot gases with fresh
air as they flow away from the fire source. This is a similar mixing process that takes
places in a vertical turbulent fire plume. The scale analysis of an inert mixing plume
[24, 25] gives α of 2/3 and β of 5/3.
The experimental and theoretical work by Alpert [26] provides the full expression
and the coefficients valid for an axi-symmetric, unconfined ceiling jet as a function
of radial distance from the fire centre. The correlation is given below in Eq. (5.4).
Alpert found experimentally that α and β are both 2/3, and that there is a
dependence on the inverse of the ceiling height (thus yielding a combined power
law coefficient for the spatial distance of 5/3 as predicted by the scale analysis).
%�& − ∞ = 5.38�� )⁄ �+ ,⁄- (5.4)
where %�& is the maximum ceiling jet temperature(°C)
∞ is the ambient temperature (°C)
� is the total heat release rate (kW)
) is the distance from the centre of the fire (m)
- is the floor to ceiling height (m)
118
The Alpert correlation uses the total heat release rate, rather than its convective
portion which is related to buoyancy. This is due to the fact that the heat release
rates of pool fires, which were the basis of the correlation, are often reported as total
values and not convective [27]. The specific pool fires used for the development of
the Alpert correlations were alcohol pool fires, in which the radiative fraction is
negligible. Therefore, for application in this methodology, the heat release rate is
assumed to be purely convective, i.e. the radiative fraction is taken to be zero.
Alpert gives a piecewise equation for maximum ceiling jet temperatures to describe
the near field (r/H ≤ 0.18) and far field (r/H > 0.18) temperatures. But only the far
field equation is used here. The methodology assumes the near field to be the flame
temperature and does not use the expression given by Alpert. If the results of Eq.
(5.4) exceed the specified near field temperature at any point, they are capped at the
flame temperature.
This correlation was used in previous work of this methodology [4, 13, 18]. Its use
for horizontally travelling fires requires the further assumption that the coefficient,
J, does not change significantly when the linear distance, I, replaces the radial
distance, ), given by Alpert (planar vs. axi-symmetrical configurations). Therefore,
the linear distance, I, is used in the methodology.
It is also noted that the correlation assumes an unconfined ceiling with no
accumulated smoke layer. However, these strict limitations are ignored in the
application to this methodology. This has been done as it is a simple correlation and
was chosen to provide an approximate and straightforward calculation of the
temperature field that is sufficient to progress the development of the methodology.
Further sophistication and accuracy could be added to this framework as needed.
As a point of comparison between the axi-symmetric ceiling jet correlation and a
planar case, a set of CFD simulations were run using FDS v5.5.3. The simulations
examined the temperature decrease with linear distance from a 147MW fire (the
119
25% fire size examined in Section 5.5) over a 28m wide strip located at one end of a
large compartment 42m long by 28m wide and 3.6m high (see Section 5.4 for
details). A grid sensitivity study was conducted to ensure good resolution and the
final cell size was set at 40cm. Three cases were investigated: 100% ventilation
opening (the whole façade is open), 50% ventilation opening, and 25% ventilation
opening. While very different ventilation scenarios were investigated, Figure 5.3
shows that the ceiling jet correlation provides a similar decay with distance (similar
P value) to the FDS models. The temperature agreement is better at larger distances.
Figure 5.3: Comparison of Alpert’s ceiling jet correlation with three FDS models of varying
ventilation for a 147MW, 28m wide fire (25% fire size) burning at one end of the
compartment (see Section 5.4 for details).
The values of P for the three FDS curves are 0.605 for 100% ventilation, 0.502 for
50% ventilation, and 0.463 for 25% ventilation. These values are similar to the 2/3 P
value from Alpert’s correlation. The modelling results provide confidence that the
ceiling jet correlation, while not exactly capturing the fire dynamics of each scenario
of interest here, gives appropriate and conservative results.
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35 40 45
Tem
pe
ratu
re (o
C)
Distance (m)
Alpert Correlation
FDS - 100% Ventilation
FDS - 50% Ventilation
FDS - 25% Ventilation
Near Field Far Field
120
The previous work of this methodology [4, 13, 17, 18] took a single representative
temperature for the far field for each fire size, independent of distance. The work in
this paper, however, relaxes this simplification and allows for spatially varying far
field temperatures to be carried into the heating calculations. While this creates
more information to pass to the structural analysis, it provides a more accurate
representation of the fire dynamics for each scenario, which may be particularly
important for analyses of whole frame behaviour.
5.3.3 Spatial Discretisation
It is assumed that the fire extends the whole width of the building and travels in a
linear path along the structure’s length. Other fire paths are possible but results
shown in [4] demonstrate that they do not greatly alter the structural response. Thus
a single linear path is chosen for this further development of the methodology. As
the far field temperature is assumed uniform along the width of the building but
varies along its length for the assumed linear path, the problem is treated as one-
dimensional. Thus the far field temperature for any given fire size can be calculated
at any position in the structure by its linear distance from the fire. This discretisation
is similar to the strips examined by Clifton in his Large Firecell Model [28].
The fire is assumed to travel at a constant spread rate, Q, across the floor plate. This
is calculated by Eq. (5.5) and is related to burning time and fire size.
Q = R�"# (5.5)
where Q is the spread rate (m/s)
R� is the length of the fire (m)
Given that there is a fixed local burning time (based on the assumption of a uniform
fuel load density and a constant heat release rate per unit area, as explained in
Section 5.3.1), there is a one-to-one relationship between fire size and spread rate.
121
This corresponds with the logic that the bigger the fire, the faster it moves. For
example, a fire that is 50% of the floor area (R� = 0.5R) would have a spread rate five
times faster than a 10% fire (R� = 0.1R3, as the local burning time is the same for
both.
To track the fire location over time and enable calculation of the far field
temperature at various distances, the building is broken up into numerous nodes,
each with a fixed width ∆I (also referred to as the grid size). Each node has a single
far field temperature at any given time. Therefore the more elements that are used,
the better resolved the far field temperature is (see Section 5.5.2). As the fire travels
across the floor plate, nodes go from being unburnt, to on fire, to burnt out.
Figure 5.4 illustrates the one-dimensional discretisation of the building showing the
grid size (∆I), total length (R), fire length (R�), far field distance (I��), node
references, and the leading and trailing edges of the fire. The near field distance is
half the fire length, while the far field distance (I��) is taken from the fire centre to
the node being examined (node S).
Figure 5.4: Illustration of spatial discretisation, showing the nodes of grid size, ∆I, and the
characteristic lengths of the problem. The fire (orange) travels at spread rate, Q,
towards the unburnt nodes (white), leaving burnt-out nodes (grey) behind.
Δx Lfs
Node 1 Node iNode 2 Node 3 Node 4
xffxi
Node i + 1 Node nNode n - 1Node i - 1
L
Node 5
Trailing Edge Leading Edge
122
Each node can be described by its index, varying from 1 to n. The distance, Ib, from
a fixed reference point, taken here as the left end of the structure where the fire is
assumed to start, to another point can be described by Eq. (5.6).
Ib = 2S − 0.53∆I (5.6)
where Ib is the position relative to the end of the structure (m)
S is the node reference (-)
∆I is the grid size (m), also given by R �⁄
The relative positions of the fire location and the node can be tracked over time to
give a full transient evolution of the temperature field, including the passage of the
near and far fields (see Figure 5.1b and Figure 5.2). In order to adequately resolve
the movement of the fire, the time step, ∆"∗, is determined by Eq. (5.7).
∆"∗ = ∆IQ (5.7)
This definition allows the time step to capture the movement of the fire from one
node to the next. If the time step is longer than that calculated by Eq. (5.7), then
important information is lost. However, note that there is no benefit in making a
smaller time step. This is because a node cannot be partially occupied by the fire,
and thus each node has only one temperature for each time step. A finer time step
would yield consecutive times with the same temperature. Therefore the time step
in this work is always set by Eq. (5.7).
The time the fire spends at one node location, "b, is the sum of the travel time across
the node plus one local burning time. The whole node is assumed to start burning
when the leading edge of the fire enters from the near side. Then the whole node is
burnt out when the trailing edge of the fire passes the far side. This is given by Eq.
(5.8).
123
"b = ∆IQ + "# (5.8)
As the fire travels across � − 1 nodes (the initial condition has node 1 burning at
" = 0), the total burning duration, "EFE�G, is the travel time across the rest of the floor
plate plus one burning time. This fact, plus noting that � = R ∆I⁄ , means the total
burning duration is given by Eq. (5.9).
"EFE�G = "# cR − ∆IR� + 1d (5.9)
As can be seen from Eq. (5.9), the total burning duration is a multiple of the local
burning time. This multiple of the local burning time is greater for smaller fire sizes,
meaning longer total burning durations. This explains why travelling fires account
for the longest burning fires that can take place in a large compartment and, indeed,
corresponds well to those observed in accidental fires [3].
Note that the total burning time also depends on the grid size (due to the initial
condition). The largest grid size that can be used to ensure that a given fire size is
fully resolved is ∆I = R�. A larger grid size would lead to the fire only occupying a
portion of any node, which is inconsistent with the assumptions of this
methodology. Placing this maximum grid size in Eq. (5.9), gives a total burning time
of "EFE�G = "#�R R�⁄ �. For example, the total burning duration for a 25% fire is 76min,
which is four times the local burning time (19min). The approach taken in earlier
work [4, 13, 18] used the largest grid size only and therefore had total burning
durations along these lines. However, as the grid size is reduced, the total burning
duration increases. The longest possible total burning duration, denoted as "EFE�G∗ , is
the limit of "EFE�G as the grid size approaches zero (the smallest possible grid size), as
given in Eq. (5.10).
"EFE�G∗ = lim∆&→g "EFE�G = "# c RR� + 1d (5.10)
124
This means that the total burning duration is up to one local burning time longer
with a fine grid resolution than with a coarse one. For the same 25% fire size
example, the total burning duration with a very well resolved grid would approach
five times the local burning time, or 95min. This additional burning time, which was
not considered in previous versions of the methodology, represents the time period
of initial fire growth before the fire reaches its full size and the final stages of the fire
as it burns out and is again smaller than its full size. This is not accounted for in the
coarse grid case, which assumes the fire initialises and burns out at its peak size.
5.4 Application to a Generic Structure
The travelling fires methodology presented here is applied here to a case study of a
generic concrete frame, shown in Figure 5.5. The structure is based on that used in
Law et al. [4], but without the central core. The compartment is 42m long, 28m wide
and 3.6m high. There are six structural bays along the length of the building, and
four across its width. Each bay is 7m x 7m. The fire is assumed to ignite at one end
of the structure, occupy the full width and burn along its length over time as
illustrated in Figure 5.5.
A family of fires was investigated with sizes ranging from 1% to 100% of the floor
plate. A selection of fires is given in Table 5.1, showing the fire size and area, the
heat release rate calculated from Eq. (5.1), the maximum total burning duration
from Eq. (5.10), and the spread rate from Eq. (5.5).
125
Figure 5.5: The generic concrete structure used for the case study.
Fire size hi (m2) j (MW) kklk�m∗ (min) n (m/min) 1% 11.8 5.9 1919 0.02
2.5% 29.4 14.7 779 0.06
5% 58.8 29.4 399 0.11
10% 117.6 58.8 209 0.22
25% 294 147 95 0.55
50% 588 294 57 1.1
75% 882 441 44.3 1.7
100% 1176 588 38 2.2
Table 5.1: A selection from the family of fires.
The burning durations of the larger fire sizes are of the same order of magnitude as
those predicted by the traditional methods [2]. The smaller fire sizes have burning
durations on the order of those observed in large, accidental fires [7, 8, 9]. For
example, the One Meridian Plaza fire in Philadelphia in 1991, which had horizontal
and vertical flame spread, lasted for almost 19 hours [29]. The range of spread rates
from the family of fires also corresponds well with physical values. Quintiere [30]
gives the rough order of magnitude of lateral fire spread on thick solids as 0.1cm/s
28m
654321
Far field
(not yet burnt)
Far field
(burnt out)
Near field
(fire)
Travel Direction
Bay References
Column
42m
Ignition at this side
126
(0.06m/min) and of “forest and urban fire spread” between 1 and 100cm/s (0.6 to
60m/min). This again highlights the advantage of considering a range of fire sizes in
this methodology, as the burning duration and spread rate of an accidental fire
cannot be calculated a priori.
The family of fires created was used to generate transient gas phase temperature
fields across the structure. The temperature fields were then used as input to
calculate the resulting in-depth concrete temperature at the rebar location as a
simple measure of structural performance. The hotter the rebar temperature, the
poorer the structural performance is deemed to be. One-dimensional conductive
heat transfer inside the material was considered with boundary conditions for
convective and radiant heating from the gas phase as well as reradiation. The heat
transfer was solved by means of finite differences, as detailed in Appendix A. Law
et al. [4] showed that the average rebar temperature across a bay is a more critical
parameter for the structural response than that of a single point. Therefore to obtain
the bay average rebar temperatures (referred to as the bay temperature), the average
across the whole bay is calculated from results of the one-dimensional, in-depth
heat transfer method at each node.
An alternative to this approach would be to use a three-dimensional heat transfer
method and then calculate the full structural response by use of a detailed Finite
Element Model (FEM). This was the approach taken in the work done by Law et al.
[4]. For comparison, the bay average temperature results of the method used in this
paper were found to be between 7 to 15% higher than that calculated by Law et al.
Therefore this method is deemed appropriate, especially considering the differences
in comparison to a FEM approach (one vs. three-dimensional heat transfer, constant
vs. temperature dependent concrete properties, and varying heat transfer
formulations). The simple approach used here allows for rapid calculation of a large
variety of parameters which would be computationally restrictive to do with full
FEM analyses.
127
5.5 Parameter Sensitivity Study
One aim of this methodology is to allow fire safety engineers to interface with
structural fire engineers to determine the most appropriate design fire scenarios
prior to the detailed structural analysis. It is the intent of this sensitivity study to
highlight the important parameters that should be considered in design.
The parameter values for the base case scenario and the ranges investigated are
given in Table 5.2. Unless specified otherwise, the base case values are used. The
study includes building, physical, and numerical parameters. Building parameters
are the actual quantities related to the building structure and its contents. Changes
in these parameters come from differing building designs or uses. Physical
parameters are those related to the temperature field and heat transfer mechanisms.
Numerical parameters are those required to generate the temperature fields and
heating but without physical meaning, such as the grid size. These last two sets of
parameters do not depend on the building design or its use, but on the theoretical or
numerical aspects of the methodology. As the fire size is the fundamental input
variable to the methodology, it is not classified as a parameter but a variable.
The following sections present the sensitivity of each of the parameters in Table 5.2.
5.5.1 Fire Size
Figure 5.6a shows the variation of peak rebar temperature with fire size ranging
from 1.25% to 100% for a grid size of 0.2625m. This grid size was selected as it
divides evenly amongst a large number of fire sizes.
128
Parameter Range Base Case Parameter
Type Comment
Fire Size
(��)
1% – 100% of
floor plate 10%
Main
variable
Range is parametrically generated to
cover all possibilities. Base case value
determined by analysis in Section 5.5.1.
Grid Size
(∆I) 0.21 – 42m 1.05m Numerical
Range is to have a well resolved grid for
the smallest fire (1%) to the coarsest
possible for the largest fire (100%). Base
case value determined by analysis in
Section 5.5.2.
Rebar Depth
(56) 20 – 50mm 42mm Building
Range taken to be representative of
typical range in real buildings. Base case
value as per the design of the case study
building [4].
Bay Location 1st – 6th bay 6th bay Building
Range is all six bays of the structure. Base
case value selected as it is the most
onerous for the structure as shown in
Section 5.5.4.
Bay Size
(R#) 1.05 – 21m 7m Building
Range is from the bay being the base case
grid size (1.05m) to half the structure’s
length (21m). Base case value as per the
design of the case study building [4].
Fuel Load
Density
($�)
285 –
1500MJ/m2 570MJ/m2 Building
Range covers sparsely furnished
(classroom) to densely loaded (library)
spaces. Base case value is taken as the 80th
percentile design value [19] for office
buildings.
HRR per Unit
Area
(� ") 200 –
800kW/m2 500kW/m2 Building
Range taken for representative values of
real fuels in non-industrial buildings [31].
Base case value is taken as densely
furnished office [20].
Emissivity
(o) 0.2 – 1 0.7 Physical
Range taken to test sensitivity; however
values in an accidental fire are expected
to be above 0.5. Base case value is taken
from Eurocode guidance [2].
Convective
Coefficient
(ℎK)
10 –
100W/m2 K 35W/m2 K Physical
Range taken to represent bounds in a fire
condition [32]. Base case value is taken
from Eurocode guidance [2].
Near Field
Temperature
(/�)
800 – 1200°C 1200°C Physical
Range taken to represent bounds of
compartment flame temperatures [23,
24]. The base case is taken as the upper
end of the range to represent worst case
conditions and provide similarity to
earlier work [4].
Structural
Material
Concrete or
Steel Concrete Building
Two structure types have been
considered: concrete and steel. This paper
predominately focuses on concrete, but
some comparison is made for three steel
beams: unprotected, 60min fire rated, and
120min fire rated.
Table 5.2: Parameter values for the base case and ranges investigated.
129
(a)
(b)
Figure 5.6: (a) Peak bay temperatures vs. fire size for ∆x = 0.2625m; (b) Time for bay rebar
temperatures to reach 400°C on a log scale for time.
300
350
400
450
500
550
600
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Pe
ak
Ba
y T
em
pe
ratu
re (o
C)
Fire Size
10
100
1000
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Tim
e t
o 4
00
oC
(min
)
Fire Area
130
Fire sizes between 5% and 20% result in the largest bay temperatures (between 538
and 548°C) and thus are the most challenging for the structure. The maximum peak
bay temperature is 548°C for a 10% fire. Note that both a very small fire (2%) and a
very large fire (100%) result in the same peak bay temperature of 410°C. The smaller
fire sizes have long durations, but relatively low far field temperatures. The larger
fire sizes have higher far field temperatures, but for shorter durations. The
maximum rebar temperature found for the 10% fire size results from an optimum
heating balance between far field temperature and duration. These results are
similar to conclusions of work previously reported [4, 13].
Because the most challenging scenario is the 10% fire size, it is used as the base case
for the rest of this sensitivity study.
Figure 5.6b gives the time for bay temperatures to reach 400°C. A reference value of
400°C was selected for comparison of heating times as this was a bay rebar
temperature reached by all but the smallest fire size (1.25%). It shows that the larger
fire sizes reach this temperature more quickly than the smaller ones, even though
they ultimately do not reach the same peak temperature. Note, however, that the
time for the bay rebar to reach a specified temperature for a travelling fire is
dependent on the location of the bay relative to the fire’s path, i.e. the time of near
field arrival relative to the total burning duration. This is explored further in Section
5.5.4.
5.5.2 Grid Size
The grid size was varied in a series of cases to ensure that the number of nodes in
the discretisation scheme is high enough to properly resolve the dynamics of the
problem. The grid size has an impact on three parts of the methodology: the
resolution of the far field temperature in Eq. (5.4), the total burning duration in Eq.
(5.9), and the resolution of a bay (R# ∆I⁄ ). The impacts of these parameters are
explored below.
131
Figure 5.7 shows the error of the peak bay temperature relative to the finest grid
against varying grid sizes. The finest grid size used for any calculation was 0.21m,
which is fine enough to include more than one node across the smallest fire size
(1%). The smaller the grid size, the lower the error, thus proving the grid
independence of the model. A grid size of 1.05m gives an error of approximately 1%
for several fire sizes, including the base case 10% fire size, and therefore has been
selected as the base case grid size.
Figure 5.7: Error in the peak bay temperature relative to finest grid (∆I = 0.21m) vs. grid
size for a range of fire sizes.
The evolution of the gas temperature and the resulting bay temperatures for the last
bay (Bay 6) at the far end of the structure (node n) are shown in Figure 5.8 for three
grid sizes: coarse (∆I = 10.5m), medium (∆I = 2.1m), and fine (∆I = 0.21m). For the
course grid, the peak bay temperature was lower (by 63°C, difference of 12.7%) and
arrived earlier (by 15min, difference of 15.6%) than for the fine grid which resulted
in a peak bay temperature of 514°C at 96min after ignition. The results of the
medium grid are very similar to the fine grid (517°C peak bay temperature at
0.01%
0.10%
1.00%
10.00%
0.1 1 10
Tem
pe
ratu
re E
rro
r
Δx (m)
5% Fire
10% Fire
25% Fire
75% Fire
132
95min). Given the differences in structural heating resulting from the coarse and
fine grids, and the similarities of heating from the medium and fine grids, the model
is concluded to be grid independent for grid sizes of 2.1m and finer.
Figure 5.8: Gas phase and resulting bay temperatures vs. time at the far end of the
structure (Bay 6) for coarse (∆I = 10.5m), medium (∆I = 2.1m), and fine
(∆I = 0.21m) grids.
The change of slope in the gas phase curves at 19min is due to the growth of the fire
to its full size prior to that time. Note that these bay temperature results are for the
last bay in the compartment. Thus when the fire ends, the gas temperature returns
immediately to ambient. After that, the rebar is still heated from the thermal wave
passing through the slab but then slowly cools at a rate controlled by the heat
transfer in the concrete. This cooling phase and its relationship to whole frame
response during a fire are of great importance to structural engineering [33, 34, 35].
The more well resolved the compartment, the longer the total burning duration is,
eventually approaching "EFE�G∗ as can been seen from Eqs (5.9) and (5.10). For the gas
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100 120
Tem
pe
ratu
re (o
C)
Time (min)
Δx=10.5m gas
Δx=2.1m gas
Δx=0.21m gas
Δx=10.5m rebar
Δx=2.1m rebar
Δx=0.21m rebar
Δx = 2.1m
(gas phase)
Δx = 10.5m
(gas phase)
Δx = 0.21m
(gas phase)
Δx = 10.5m
(rebar)
Δx = 2.1m
(rebar)
Δx =0. 21m
(rebar)
133
phase temperatures shown in Figure 5.8, "EFE�G is 80% of the theoretical limit, "EFE�G∗ ,
for the coarse grid ("EFE�G is 76min compared to "EFE�G∗ which is 95min), 96% for the
medium grid ("EFE�G of 91.2min), and 99.6% for the fine grid ("EFE�G of 94.6min). This
is one reason for the earlier and lower peak bay temperature seen for the coarse
grid. As an additional check on the impact of this fraction of the theoretical
maximum burning duration, one local burning time was added to the coarse grid
case (spread evenly amongst the three far field components of the gas phase
temperature-time curve), bringing "EFE�G to 95min and equal to "EFE�G∗ . The peak bay
temperature from this check was 477°C (7.5% lower than that from the finest grid) at
100min (4.2% later), instead of the previous 451°C peak and 15min time difference.
Thus, the impact of the temporal delay introduced by coarse grids can be easily
quantified.
Coarse grids that are on the same order of length as a structural bay could also
affect the bay temperatures. This is explored in Section 5.5.4.
5.5.3 Rebar Depth
The depth of rebar is a fundamental design variable for any concrete structure.
Typical rebar depths are between 20 and 60mm. A structural engineer would
usually establish the rebar depth of a structure before its fire performance is
analysed in detail. However, it is worth understanding the impact of rebar depth on
peak bay temperatures, as it could make a significant difference in the design and,
subsequently, the performance and cost of the structure.
Figure 5.9a shows the gas phase and resulting bay temperature vs. time for various
rebar depths for the base case. Figure 5.9b shows the peak bay rebar temperature for
varying rebar depth and fire size, for a grid size of 0.21m. The results show the
logical result that the shallower the rebar, the higher its temperature.
134
(a)
(b)
Figure 5.9: (a) Gas phase and bay temperatures for rebar depths of 20, 30, 42 and 50mm;
(b) Peak bay temperature vs. fire area and rebar depth for ∆I = 0.21m.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250
Tem
pe
ratu
re (o
C)
Time (min)
Gas Phase at Bay 6
20mm Rebar
30mm Rebar
42mm Rebar
50mm Rebar
Pe
ak
Ba
y T
em
pe
ratu
re (
oC
)
135
The 10% fire size results in the maximum peak bay temperature for all rebar depths
except the 50mm depth, which has its maximum at the 5% fire size. This is due to
the increased importance of the pre-heating and post-heating of the rebar from the
far field, which is longer for smaller fires. A rebar depth of 42mm is used for the
base case as this was the design value for the similar structure in [4].
5.5.4 Bay Location and Bay Size
As discussed above, the bay temperature is a critical parameter for structural
response. Figure 5.10 shows the sensitivities of the bay location and bay size. Figure
5.10a gives the temperature-time curves for each bay in the compartment (see Figure
5.5 for bay numbering). Figure 5.10b gives the peak bay temperature as a function
bay length for three fire sizes (5%, 10%, and 25%). The fire begins in Bay 1 and
travels across the structure, eventually ending in Bay 6.
Figure 5.10a shows that the peak bay temperature increases with distance from the
ignition location. This is because the peak temperatures are always caused by
exposure to the near field, but are also dependent on the bay temperature at the
time of near field arrival. The bay temperature at the time the fire arrives is
dependent on the exposure duration and temperatures of the far field. As each
subsequent bay along the structure is exposed to longer pre-heating times prior to
the arrival of the near field, the hottest peak bay temperature is found in the final
bay (Bay 6).
This conclusion can be generalised, stating that the peak rebar temperature in a
structure will occur at the final burning location of the fire. This is a significant
result, as it means that the exact travel path of a fire does not need to be known if
the peak rebar temperature is the variable of interest for the structural analysis. This
is beneficial for design, as the path cannot be known a priori as there are many
possible paths of fire travel depending on ignition location, early fire development
and subsequent glazing failure.
136
(a)
(b)
Figure 5.10: (a) Bay temperatures vs. time for each bay in the structure along its length;
(b) Variation of peak bay temperature with bay length for 5%, 10% and 25% fire
sizes.
0
100
200
300
400
500
600
0 50 100 150 200 250
Ba
y T
em
pe
ratu
re (o
C)
Time (min)
Bay 1
Bay 4 Bay 5 Bay 6
Bay 2Bay 3
400
440
480
520
560
600
0 5 10 15 20 25
Pe
ak
Ba
y T
em
pe
ratu
re (o
C)
Bay Length (m)
5% Fire
10% Fire
25% Fire
137
Thus for design, if the structural engineer can identify particular areas of the
structure that are most vulnerable to the effects of elevated rebar temperature, then
it can be conservatively assumed that the fire reaches this location last, thereby
producing the most onerous fire environment for that part of the structure. Note
that other structural variables are important in travelling fires (see [4]) and that the
role played by the heating and cooling phases, for example, are not directly
captured by the peak bay temperature alone.
Figure 5.10b shows the impact of bay size on bay temperature. The bay size was
varied from 1.05m (the smallest possible bay size for the base case grid size, as there
is only a single node per bay) to 21m (half the length of the structure, which is
deemed to be beyond a realistic upper bound). The results indicate that the larger
the fire, the less impact the bay size has on the peak bay temperature. This is due to
the ratio between fire size and bay size. For bay sizes that are smaller than the fire
size, the full bay is exposed to the near field at once. Given that much of the range in
bay size variation is less than the fire size for the 25% case (the largest fire examined
here, with R� = 10.5m), little impact on peak temperatures is expected from variation
of bay size. However, for the smaller fire sizes, many of the bay lengths examined
are greater than the fire lengths (2.1m for the 5% fire and 4.2m for the 10%).
Therefore impact of bay size is to be expected in these cases.
The results also show that the maximum peak bay temperatures occur nearly, but
not exactly, when the bay size is equal to the fire size. This is due to the balance of
higher far field temperatures prior to the fire arriving and lower far field
temperatures after the fire passes. There is a small effect of the grid size on the peak
value, but as the temperature differences are small (on the order of 10°C) it is not
deemed significant.
138
5.5.5 Fuel Load Density and Heat Release Rate per Unit Area
Eq. (5.2) gives the local burning time as a function of the fuel load density and heat
release rate per unit area. The local burning time, in turn, affects the total burning
duration. The higher the fuel load, the longer the local burning time and, thus, the
longer the total burning duration. The heat release rate per unit area also impacts
the burning times. The higher the heat release rate per unit area, the shorter the local
burning time and total burning duration of a fire. However, the heat release rate per
unit area also has an impact on the total heat release rate for a given fire size and,
therefore, the far field temperatures. This means that as it reduces the total fire
duration, it also increases the gas phase temperatures to which the structure is
exposed.
The amount of fuel in a building significantly alters the dynamics of a fire. The fuel
load varies greatly for building types and guidance exists to provide typical ranges
[2]. The base case fuel load was taken as the 80th percentile value for office buildings
[19]. The range of values for the sensitivity study varies from sparsely furnished
(classroom) to densely loaded (library) spaces according to [2]. The heat release rate
per unit area is a fundamental characteristic of a fire. The range selected here
corresponds to that measured for a variety of fuels that could be expected in a
typical office building [31], but excludes very high values that might be associated
with rack storage or other industrial usages. The base case value is taken from [20]
and is the same used in earlier work [4].
Figure 5.11 shows the variation of peak bay rebar temperature with fuel load
density for heat release rates per unit area of 200, 500, and 800kW/m2.
Denser fuel loads result in higher peak bay rebar temperatures. The opposite trend
is observed for the heat release rate per unit area, i.e. the lower the heat release rate
per unit area, the higher the peak bay rebar temperatures. Both of these trends can
be explained by the increase in time that results from in an increase in fuel load or
139
decrease of the heat release rate per unit area. While the total heat release rate
increases for a higher heat release rate per unit area, these results suggest that the
effect of the reduction in fire duration is more important than the effect of the far
field temperature on the structural heating. This is due to the linear relationship
between heat release rate per unit area and time and the 2/3 power relationship
between heat release rate and far field temperature.
Figure 5.11: Peak bay temperature vs. fuel load density for a range of heat release rates per
unit area.
5.5.6 Heat Transfer
Because it is difficult to quantify specific values of the overall heat transfer
coefficient and emissivity in a fire, the sensitivity of these parameters has been
examined here. The convective heat transfer coefficient of the exposed side of the
concrete slab was varied from 10 to 100W/m2 K to represent the bounds typically
expected in a compartment fire [48]. The material emissivity was varied from 0.2 to
1. For typical concrete reradiation at high temperatures, the effective emissivity is
likely to be high, but 0.2 has been examined as a lower bound. The gases are
350
400
450
500
550
600
650
700
750
0 200 400 600 800 1000 1200 1400 1600
Pe
ak
Ba
y T
em
pe
ratu
re (o
C)
Fuel Load Density (MJ/m²)
200 kW/m²
500 kW/m²
800 kW/m²
140
assumed to have an emissivity equal to 1, and the material absorptivity is assumed
to be equal to the emissivity. The base case values of both heat transfer parameters
were taken according to Eurocode 1 guidance [2].
Figure 5.12 plots peak bay temperature against the convective heat transfer
coefficient for varying values of emissivity and two rebar depths. A shallow rebar
depth (20mm) was examined, in addition to the base case value, to include a
scenario of reduced importance of the conductive heat transfer.
Figure 5.12: Peak bay temperature vs. convective heat transfer coefficient for a range of
material emissivities and rebar depths.
The results indicate that the peak bay temperatures are only marginally affected by
the heat transfer parameters at either of the two rebar depths studied. The lower
temperatures that result from the lower emissivities indicate that concrete heating is
dominated by radiation in the base case.
400
500
600
700
800
900
0 20 40 60 80 100
Pe
ak
Ba
y T
em
pe
ratu
re (o
C)
Convective Heat Transfer Coefficient (W/m²K)
ε=0.2, 42mm rebar
ε=0.5, 42mm rebar
ε=0.7, 42mm rebar
ε=1, 42mm rebar
ε=0.2, 20mm rebar
ε=0.5, 20mm rebar
ε=0.7, 20mm rebar
ε=1, 20mm rebar
141
5.5.7 Near Field Temperature
For the sake of conservatism, the methodology assumes that the near field
temperature is the peak flame temperature measured in large fires. The sensitivity
of bay temperatures to this assumption is studied here. Peak temperatures in small
fires have been measured in the range of 800 to 1000°C [23], while those in larger
compartments have been found to be up to approximately 1200°C [24]. The FDS
simulations of a localised 147MW fire in a large compartment shown in Figure 5.3
agree with this range and predict peak near field temperatures ranging from 800 to
1050°C, depending on the ventilation scenario. Therefore the near field temperature
has been varied from 800 to 1200°C, with the base case value at the upper end of the
range to account for worst case conditions and overcome the uncertainty associated
with the prediction and measurement of flame temperatures. Figure 5.13 shows the
bay temperature evolution over time for varying near field temperatures at Bays 2
and 6.
Figure 5.13: Bay temperature vs. time for near field temperatures between 800 and 1200°C at
Bays 2 and 6.
0
100
200
300
400
500
600
0 50 100 150 200 250 300 350 400
Ba
y T
em
pe
ratu
re (o
C)
Time (min)
800°C Bay 6
900°C Bay 6
1000°C Bay 6
1100°C Bay 6
1200°C Bay 6
800°C Bay 2
900°C Bay 2
1000°C Bay 2
1100°C Bay 2
1200°C Bay 2
Bay 2
Bay 6
142
The results show that a near field temperature variation of 400°C (from 800 to
1200°C) produces a peak bay temperature range of approximately 130°C. The results
are similar for both bays. The near field temperature assumed has no impact on the
structural heating in the far field region, but does have an important overall effect
on the predicted fire resistance of the structure. However, given that the design
value is taken at the upper end of the physical range, it means results from this
methodology can be deemed conservative.
5.5.8 Steel Structure
In addition to the base case concrete structure, the heating of a typical steel beam is
also examined. The steel beam studied was selected to be representative of typical
section sizes used in real buildings. Dimensions of the beam are given in Figure
5.14. The beam has been assessed with three levels of fire protection: unprotected,
fire rated to 60min, and fire rated to 120min. For quantification of its heating, it is
assumed that there is a slab above the top flange of the beam and thus it is only
heated on three sides.
Figure 5.14: Dimensions of the steel beam section analysed.
The heat transfer to the beam was calculated utilising a lumped mass approach and
is given in Appendix A. For the purposes of this analysis, it is assumed that the steel
beam is perpendicular to the direction of fire propagation and thus is exposed to the
same gas temperature along its full length at any given time. This is done because
15mm
15mm
8mm
200mm
350mm
Not to scale
143
using a single beam temperature as a surrogate for structural response is not valid
for a beam exposed to a varying temperature along its length. This methodology
could also be used for calculation of the distribution of steel temperatures along the
beam axis as the rate of conductive heat transfer in steel is much lower than the
spread rate of a travelling fire. However determining the structural response of that
scenario would require the adoption of a two or three-dimensional structural
analysis method. Nonetheless, the single point heat transfer calculations used here
provide insight into the differences in heating of the three types of steel beam, as
compared to the concrete slab.
Figure 5.15a shows the resultant peak steel temperatures for the three beam types at
the far end of the final structural bay (Bay 6) for a grid size of 0.21m. The fine grid
resolution was used to best match the node size to the physical size of the steel
beam.
It can be seen that the steel temperatures of the unprotected beam reach the near
field temperature for all fire sizes. This is due to the low thermal inertia and high
conductivity of the unprotected steel. The protected beam temperatures follow a
similar trend to that of the concrete structure. The maximum temperature recorded
for the 60min rated beam is from a 10% fire size and for the 120min beam from a 5%
fire size.
Figure 5.15b gives the time for the unprotected and 60min rated beams to reach
550°C (the 120min rated beams do not reach this temperature and are therefore not
shown). A critical value of 550°C was selected here as this is normally considered an
approximate temperature above which steel loses sufficient strength such that
failure of a typical simply-supported beam could occur under the loads assumed to
be applied during a fire [24]. As with the concrete bay temperatures, it shows that
the larger fire sizes reach the specified temperature more quickly than the smaller
ones, even though they ultimately do not reach the same peak temperature.
144
(a)
(b)
Figure 5.15: (a) Peak steel temperature vs. fire size for unprotected, 60min rated, and 120min
rated steel beams at the far end of Bay 6 for a grid size of ∆I = 0.21m; (b) Time
for the unprotected and 60min rated steel beams to reach 550°C on log scale for
time.
0
200
400
600
800
1000
1200
1400
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Ste
el T
em
pe
ratu
re (o
C)
Fire Size
Unprotected
60min
120min
10
100
1000
10000
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Tim
e t
o 5
50
oC
(min
)
Fire Area
Unprotected
60min
145
The unprotected beam reaches 550°C between 29min (for the 1% fire) and 34min (for
the 50% fire) faster than the 60min rated beam. Fire sizes above 50% do not reach
550°C for the 60min rated beam. Note, however, as with the concrete rebar heating,
the time for the steel beam to reach a specified temperature for a travelling fire is
dependent on the location of the bay relative to the fire’s path, i.e. the time of near
field arrival relative to the total burning duration.
Figure 5.16 shows temperature-time curves for the gas phase and steel for all three
beam types considered at two different locations in the structure. The unprotected
steel temperature follows the gas phase temperature very closely, for the reasons
given above. The peak steel temperatures are very similar for both locations, with a
slightly higher peak reached for the midpoint of Bay 2 for the 60min rated beam.
This lack of sensitivity to steel location is different from that observed in concrete
(see Figure 5.10a)
Figure 5.16: Temperature vs. time for the gas phase plus all three steel beam types at the
midpoint of Bay 2 and the far end of Bay 6.
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300
Tem
pe
ratu
re (o
C)
Time (min)
Bay 6, Gas
Bay 2, Gas
Bay 6, Unprotected Steel
Bay 2, Unprotected Steel
Bay 6, 60min Steel
Bay 2, 60min Steel
Bay 6, 120min Steel
Bay 2, 120min Steel
Midpoint
of Bay 2
End of
Bay 6
146
5.6 Comparison to Conventional Methods
Figure 5.17 compares the bay temperature-time curves resulting from the base case
fire scenario with those calculated from the standard fire and two Eurocode
parametric temperature-time curves [2]. One parametric temperature-time curve
assumes 100% glass breakage on the façade and the other 25%. The parametric
curves use the same thermal properties of concrete (see Appendix A for values) and
fuel load density as the base case.
Figure 5.17: Comparison of bay temperatures calculated using the base case, the standard
fire, and two Eurocode parametric temperature-time curves.
The comparison shows that the base case, which is the most onerous fire size in the
family of fires, is a more challenging scenario for the structure in terms of peak bay
temperature reached than the two parametric curves. In terms of the peak bay
temperature, the travelling fire is equivalent to 106min of the standard fire, which is
similar to the conclusions of Law et al. [4]. This is compared to the two parametric
curves, which are equivalent to 38min and 56min of the standard fire.
0
100
200
300
400
500
600
700
800
0 50 100 150 200 250
Ba
y T
em
pe
ratu
re (o
C)
Time (min)
Base Case
EC - 25% Ventilation
EC - 100% Ventilation
Standard Fire
Base case equivalent to
106 min Standard Fire
106 min
556oC
56 min38 min
363oC
252oC
147
The results presented here should be explored in more detail by a structural
engineer, as a travelling fire may lead to different structural behaviour than that
indicated by examining the peak bay temperature alone [4]. For example, whole
frame behaviour resulting from exposure to a travelling fire with portions of the
structure being heated while other areas are cooling may be different than that
suggested by the bay average results given here.
5.7 Final Remarks
Comparisons of the relative impact of all the parameters varied in the methodology
are shown in Figure 5.18. The percentage variation of each parameter from the
corresponding base case value has been plotted against the resultant percentage
change of the peak bay temperature calculated. Figure 5.18a shows the results for
the building parameters, and Figure 5.18b the physical and numerical parameters.
Fire size has been shown on both plots as it is the main variable in this
methodology.
Steeper slopes on the curves in Figure 5.18 correspond to the more sensitive
parameters. Positive values in the bay temperature change mean conditions are
more onerous on the structure than the base case and negative values less onerous.
The largest changes in bay temperature come from rebar depth, fuel load density,
fire size, and near field temperature, in this order. These are the most sensitive
parameters.
148
(a)
(b)
Figure 5.18: Relative change in bay temperature vs. percentage change in (a) building
parameters and; (b) physical and numerical parameters.
-35%
-25%
-15%
-5%
5%
15%
25%
35%
45%
-100% -50% 0% 50% 100% 150% 200% 250% 300%
Re
lati
ve
Ba
y T
em
pe
ratu
re C
ha
ng
e
Percentage Change from Base Case Value
Building Parameters
Fire Size
Rebar Depth
Fuel Load
Bay Size
-35%
-25%
-15%
-5%
5%
15%
25%
35%
45%
-100% -50% 0% 50% 100% 150% 200% 250% 300%
Re
lati
ve
Ba
y T
em
pe
ratu
re C
ha
ng
e
Percentage Change from Base Case Value
Physical and Numerical Parameters
Fire Size
Grid Size
Emissivity
Conv HT Coeff
Tnf (Concrete)
149
The rebar depth, the most sensitive parameter, is likely to be a fixed value early in
the design, but its sensitivity is worth noting for the design process of a building.
The exact fuel load density cannot be known exactly, as it is inherently variable and
may change over the lifetime of a building. Therefore a reasonable assessment of the
likely values should be made during design. It is noted that both of these
parameters would be used by many forms of structural fire assessment, whether
that be the travelling fires methodology presented in this paper or the conventional
methods.
Fire size is the main variable of this methodology, so the full range should always be
explored in a design case. While the near field temperature has a marked impact on
the bay temperatures, it is not necessary to vary this parameter for design, as the
methodology assumes the most onerous condition.
The methodology presented in this paper offers a paradigm shift in defining fire
scenarios for structural fire engineering and compliments the traditional methods.
This paper has explored the details of the method and concluded on the more
sensitive parameters that ought to be considered in design. The methodology
provides a robust platform for collaboration between fire engineers and structural
fire engineers to jointly understand a building’s structural performance in fire.
References
1 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance
testing – Part II.” Fire Technology, 14(4) 1978, pp. 304-316.
2 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on
structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.
3 Stern-Gottfried, J., Chapter 3 in: Travelling Fires for Structural Design, PhD Thesis,
School of Engineering, University of Edinburgh, 2011.
150
4 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling
fires on a concrete frame”, Engineering Structures, Vol. 33, 2011, pp. 1635-1642.
doi:10.1016/j.engstruct.2011.01.034. Open access version at:
http://www.era.lib.ed.ac.uk/handle/1842/4907
5 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.
14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204
6 Gann, R.G. et al, “Reconstruction of the Fires in the World Trade Center
Towers”, NIST NCSTAR 1-5, September 2005.
7 McAllister, T.P. et al, “Structural Fire Response and Probably Collapse Sequence
of the World Trade Center Building 7”, NIST NCSTAR 1-9, November 2008.
8 Fletcher, I. et al, “Model-Based Analysis of a Concrete Building Subjected to
Fire,” Advanced Research Workshop on Fire Computer Modelling, Santander, Spain,
2007.
9 Zannoni, M. et al, “Brand bij Bouwkunde”, COT Instituut voor Veilingheids – en
Crisismanagement, December 2008.
10 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation
Openings – Comparison of Long and Wide Enclosures”, The 6th International
Symposium on Fire Safety Science, Poitiers, France, 1999.
11 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,
“Natural Fires in Large Scale Compartments”, British Steel, 1994.
12 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of
the homogeneous temperature assumption in post-flashover compartment
fires”. Fire Safety Journal, 45, 2010, pp. 249-261.
http://www.era.lib.ed.ac.uk/handle/1842/3866
13 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel
Temperatures using Travelling Fires and Traditional Methods: Case Study for
the Informatics Forum Building”. The 12th International Interflam Conference.
Nottingham, UK, 2010.
151
14 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,
The 9th International Symposium on Fire Safety Science. Karlsruhe, Germany, 2008.
15 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and
Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th
International Symposium on Fire Safety Science, University of Maryland, USA,
2011.
16 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern
Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra
Incêndio, Natal, Brazil, 2011.
17 Rein, G. et al, “Multi-story Fire Analysis for High-Rise Buildings,” The 11th
International Interflam Conference, London, UK 2007.
http://www.era.lib.ed.ac.uk/handle/1842/1980
18 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach
to design fires for structural analysis of non-conventional buildings: A case
study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,
http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf
19 PD 6688-1-2:2007, Background Paper to the UK National Annex to BS EN 1991-
1-2.
20 TM19, “Relationships for Smoke Control”, CIBSE, 1995
21 Walton, W.D. and Thomas, P.H., "Estimating Temperatures in Compartment
Fires", Chapter 3-6 of the SFPE Handbook of Fire Protection Engineering, 3rd Edition,
2002.
22 Harmathy, T.Z., “A New Look at Compartment Fires, Part II”, Fire Technology,
Vol. 8 No. 4, 1972, pp.326-351, doi:10.1007/BF02590537.
23 Audoin, L., Kolb, G., Torero, J.L., and Most, J.M.. “Average centreline
temperatures of a buoyant pool fire obtained by image processing of video
recordings”, Fire Safety Journal, Vol. 24, 1995, pp. 167-187. doi:10.1016/0379-
7112(95)00021-K.
152
24 Drysdale, D., An Introduction to Fire Dynamics, 2nd Edition, John Wiley & Sons,
1999.
25 Heskestad, G., “Fire Plumes, Flame Height, and Air Entrainment”, Chapter 2-1 of
the SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002.
26 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire Detectors”,
Fire Technology, Vol. 8, 1972, pp. 181–195.
27 Alpert, R.L., “Ceiling Jet Flows”, Chapter 2-2 of the SFPE Handbook of Fire
Protection Engineering, 3rd Edition, 2002.
28 Clifton, G.C., “Fire Models for Large Firecells”, HERA Report R4-83, 1996, with
proposed changes in HERA Steel Design and Construction Bulletin Issue No 54,
February 2000 and updates to referenced documents, September 2008.
29 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One
Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration
Technical Report 049.
30 Quintiere, J.G, “Surface Spread of Flame”, Chapter 2-12 of the SFPE Handbook of
Fire Protection Engineering, 3rd Edition, 2002.
31 Karlsson, B., and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.
32 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, School of
Engineering, The University of Edinburgh, 2006,
http://www.era.lib.ed.ac.uk/handle/1842/1480.
33 Bailey, C.G., Burgess, I.W., and Plank, R.J., “Analyses of the Effects of Cooling
and Fire Spread on Steel-framed Buildings”. Fire Safety Journal, Vol. 26, 1996, pp.
273-293.
34 El Rimawi, J.A., Burgess, I.W., and Plank, R.J., “The Treatment of Strain
Reversal in Structural Members during the Cooling Phase of a Fire”. Journal of
Constructional Steel Research, Vol. 37, 1996, p115-135.
35 Röben, C., The effect of cooling and non-uniform fires on structural behaviour. PhD
thesis, School of Engineering, The University of Edinburgh, 2006.
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6 Conclusions and Future Work
6.1 Conclusions
Most fire tests that have been used in the development of traditional tools to define
the thermal environment for structural fire design had floor areas on the order of
only a few square metres. Larger tests, which are far fewer in number, extend to
floor areas on the order of one hundred square metres. Given that floor to ceiling
heights of real buildings are typically only a few metres regardless of floor area, the
relative impact of a compartment’s walls on the heat transfer with hot fire gases is
greatly reduced in larger compartments. In addition it is well known that radiation,
which governs flame spread in compartment fires, does not scale well. Therefore
applying data that are extrapolated from small compartment tests to large buildings
is inappropriate and has led to design methods that do not replicate real fire
behaviour at that scale.
154
One common conclusion from these small scale tests that is manifest in the
traditional structural fire design methods is that of a uniform gas phase
temperature. This homogeneous temperature assumption has been reviewed in
Chapter 2. It is shown that this assumption does not hold well. The temperature
heterogeneity that actually exists in real compartment fires does have an impact on
the heating of a structure.
However, conducting fire tests in enclosures of a size of interest for modern
building design (floor plates on the order of thousands of metres squared) is
difficult and costly. Therefore practical solutions to characterising fire behaviour in
large enclosures are needed. To this end, this thesis has developed a methodology to
characterise travelling fires for structural design. The approach used is a dramatic
departure from the traditional methods and suggests a paradigm shift in structural
fire engineering. It has been shown that this methodology both addresses
limitations in the existing methods and enables innovation in design by providing a
more realistic characterisation of the fire environment of a building.
The methodology, which is presented in Chapters 3, 4 and 5, addresses the lack of
large scale test data by examining a full range of fire sizes rather than trying to
calculate one. This fits well with the uncertainty associated in fire growth and
development in large, real buildings. The family of fires approach ensures that the
most challenging, physically possible fire scenario is considered for structural
design.
Each member of the family of fires produces far field temperatures and burning
durations related to its size. Large fires have high far field temperatures but short
durations, while small fires have low far field temperatures and long durations. The
application of the travelling fire methodology has shown that medium sized fires
(10% to 25% of the floor area) prove most challenging to a generic concrete
155
structure. These fire sizes have an optimum balance of elevated far field
temperatures and total fire duration.
The sensitivity studies conducted in Chapters 4 and 5 give insight into the effect of
varying the methodology’s input parameters. It has been shown that the most
sensitive parameters are related to the building design and use and not the
theoretical or numerical formulation of the approach. This enables practical
application of the methodology in design without the need for cumbersome
sensitivity studies of every parameter.
Accurately calculating the behaviour of a structure exposed to fire is necessary for
performance based design. However, quantifying the thermal environment created
by a fire, the resultant heating of the building elements, and the subsequent
structural response requires a broad set of skills from disparate engineering
disciplines. Therefore it has been recognised that no one individual should do this
alone and fire engineers should work with structural fire engineers to jointly solve
this problem [1, 2].
This is the spirit in which the methodology presented in this thesis has been
developed. Chapter 4 provides a good example of collaborative work between fire
and structural fire engineers. However, further collaboration is needed to better
understand the impact of travelling fires on structural performance. The travelling
fires methodology provides a robust platform for this collaborative research.
6.2 Future Work
While the travelling fires methodology developed in this thesis provides a practical
tool that can be used in design, as shown by the case studies and sensitivity analyses
in Chapters 4 and 5, further research would serve to improve it and make it more
robust.
156
6.2.1 Fire Environment
Often large scale tests in structural fire research aim to create uniform fire
conditions by providing multiple ignition points throughout evenly distributed fuel
packages. These tests also tend to be sparsely instrumented to collect data in the gas
phase. Conducting large scale tests in real buildings could greatly serve to increase
understanding of the dynamics of travelling fires. These tests should allow the fire
to grow and travel on its own and be well instrumented so the far field
temperatures and fire movement could be recorded.
Far field temperatures in this thesis have been calculated by means of an empirical
ceiling jet correlation. It has been noted that the use of this correlation is a simple
solution to a complex problem. The correlation provides temperatures as a function
of distance from the fire, but can only be applied in limited geometries.
Computational Fluid Dynamics (CFD) was used in the earliest version of the
travelling fires methodology [3] and is more readily applicable to complex
geometry; however it has drawbacks related to complexity and computational
effort. The lack of large scale test data means it is difficult to validate both the
simplistic correlations and CFD approaches taken. Work to develop better
engineering tools to calculate the far field temperature would benefit the
methodology. Such tools should consider the open nature of large, modern
compartments and not automatically assume the fires are ventilation limited [4].
On potential compromise between the correlation and CFD could be to solve the
Laplace Equation (∇+s = 0). The solution to this transport equation could be viewed
as an analogue of smoke movement. This approach, which is illustrated in Figure
5.11 for a generic structure similar to those used in Chapters 4 and 5, could explore
more complex geometry than the ceiling jet correlation, but in much less calculation
time than CFD. A Dirichlet boundary condition could represent flow out of an open
window and a Neumann boundary condition flow next to a solid wall.
157
(a) (b)
Figure 6.1: Illustration of a solution of the Laplace Equation in a generic concrete structure
showing (a) 3D contours and; (b) streamlines in plan view.
The travelling fires methodology has, to date, only focussed on horizontally
travelling fires. However, as noted in Chapter 3, accidental fires do travel vertically
as well. The sole study on the structural impact of vertically travelling fires [5], only
considers uniform fires on each floor. The methodology presented in this thesis
could be applied to vertically travelling fires as well. The time delay of spread from
one floor to the next would need to be parametrically varied. Care would need to be
taken to combine a range of such time delays with various fire sizes to ensure the
most onerous design case is identified.
6.2.2 Fire – Structure Interface
The traditional methods used in defining the thermal environment for structural fire
engineering specify gas phase temperature-time curves. The subsequent heat
transfer calculations utilise these curves to calculate the structural temperature
evolution. It was actively decided to produce gas phase temperature-time curves as
the output of the travelling fires methodology to conform to the existing heat
transfer methods used by the structural fire community. However, it is noted that
Fire
Core
x (m
)
y (m)
Re
lati
ve
Te
mp
era
ture
Ris
e (
-)
158
the actual heating of a structure results from the net heat flux to it, rather than solely
the exposure temperature. Calculation of the heat flux from a fire to a structural
element is a complex process and requires knowledge of smoke conditions such as
velocity, soot content, and layer depth. Methods have been developed to examine
this [6, 7], but this concept should be explored in relation to travelling fires.
6.2.3 Structural Response
The travelling fires methodology provides a powerful tool for structural fire
research. In collaboration with fire engineers, this methodology enables structural
engineers to examine more realistic structural response to fire than the traditional
methods. Construction types other than the concrete frame examined in Chapters 4
and 5 should be examined with this approach. Composite steel–concrete
construction is of particular interest due to its prevalence in the built environment.
A central concept of travelling fires is the non-uniform temperature field. The
impact of this on the full frame behaviour of structures should be explored.
Additionally, some structures may be more vulnerable to severe near field
conditions than others, such as post-tensioned concrete slabs. The traditional
methods do to not generally consider local near field conditions, so this should be
researched.
Small travelling fires also result in total fire durations much longer than those
calculated by the traditional methods. Thus a structure could be exposed to far field
temperatures of several hundred degrees Celsius for many hours. This could have a
significant impact on creep in steel structures and spalling in concrete frames.
Most importantly, however, the travelling fires methodology provides a framework
that allows fire engineers and structural fire engineers to jointly determine a
building’s true response in fire, thereby enabling architectural innovation and
structural optimisation.
159
References
1 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,
The 9th International Symposium on Fire Safety Science, Karlsruhe, Germany, 2008.
2 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and
Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th
International Symposium on Fire Safety Science, University of Maryland, USA,
2011.
3 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and
Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th
International Interflam Conference, London, UK, 2007.
http://www.era.lib.ed.ac.uk/handle/1842/1980
4 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern
Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra
Incêndio, Natal, Brazil, 2011.
5 Röben, C., Gillie, M., and Torero, J.L., “Structural behaviour of during a
vertically travelling fire”, Journal of Constructional Steel Research, Vol. 66, 2010,
pp. 191-197.
6 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, School of
Engineering, The University of Edinburgh, 2006,
http://www.era.lib.ed.ac.uk/handle/1842/1480.
7 Prasad, K. and Baum, H., “Fire Structure Interface and Thermal Response of the
World Trade Center Towers”, NIST NCSTAR 1-5G, September 2008.
160
161
Appendix
162
163
A Heat Transfer Calculations
This appendix provides the details of the simplified heat transfer calculations used
to quantify the rebar and steel temperatures used in Chapters 2 and 5 of this thesis.
A.1 Concrete Temperature
To determine the in-depth temperature of the concrete, a one-dimensional finite-
difference approach to the heat conduction equation was taken in explicit form, as
given by Incropera et al. [1]. It is assumed that the rebar of the concrete is the same
temperature as the adjacent concrete.
The formulation from Incropera et al. only includes surface convection, so a
radiative term was added for the surface nodes. This gives Eq. (A.1) for calculating
the exposed surface node temperature, and Eq. (A.2) for the interior nodes, and Eq.
(A.3) for the backside surface node. Chapter 2 did not use Eq. (A.3), but rather
164
assumed a sufficient depth of slab above the concrete beam such that the boundary
condition did not influence the results.
gEt: = 2∆"uKJK∆v wℎg� − gE� + �o x 4 − gE4y + zK∆v 2:E − gE3{ + gE (A.1)
bEt: = |}�bt:E + bM:E � + 21 − 2|}3bE (A.2)
/Et: = 2∆"uKJK∆v wℎ/2∞ − /E3 + �o x∞
4 − /E4y + zK∆v 2/M:E − /E3{ + /E (A.3)
where bE is the concrete temperature at time t, and location i (K) – a subscript of 0
indicates the exposed surface and a subscript of � the backside surface.
is the gas temperature (K)
. is the ambient temperature (293K)
uK is the density of concrete (2300kg/m3)
JK is the specific heat of concrete (1000J/kg K)
ℎ is the convective heat transfer coefficient (25W/m2 K for exposed surface in
Chapter 2, 35W/m2 K for the exposed surface and 4W/m2 K for the
backside surface in Chapter 5 [2])
� is the Stefan-Boltzmann constant (5.67x10-8W/m2 K4)
o is the radiative and reradiative emissivity of the material and gas
combined (assumed to be unity in Chapter 2, varied in Chapter 5)
zK is the thermal conductivity of concrete (1.3W/m K)
∆" is the time step (0.5s in Chapter 2, 10s in Chapter 5)
∆v is the element length (0.001m in Chapter 2, 0.01m in Chapter 5)
|} is the Fourier number (-), given in Eq. (A.4)
|} = zK∆"uKJK∆v+ (A.4)
165
The time step and element length were selected to meet the stability criteria
highlighted by Incropera et al. The concrete material properties were taken from
Buchanan [3] for calcareous concrete.
A.2 Unprotected Steel Beam Temperature
The unprotected steel beam temperatures were calculated by a lumped mass heat
transfer method, as given by Buchanan [3], and shown below.
∆~ = -��1
u~J~ �ℎK� − ~� + �o� 4 − ~4��∆" (A.5)
where ~ is the steel temperature (K)
is the gas temperature (K)
-� is the heated perimeter of the beam (1.284m)
� is the cross section of the beam (0.00856m2)
u~ is the density of steel (7850kg/m3)
J~ is the temperature dependent specific heat of steel (J/kg K)
ℎK is the convective heat transfer coefficient (25W/m2 K in Chapter 2,
35W/m2 K in Chapter 5)
� is the Stefan-Boltzmann constant (5.67x10-8W/m2 K4)
o is the radiative and reradiative emissivity of the material and gas
combined (assumed to be unity in Chapter 2 and 0.7 in Chapter 5)
∆" is the time step (1s in Chapter 2, 10s in Chapter 5)
All constants and steel material properties (except the emissivity) are taken from
Buchanan, including the temperature dependent specific heat.
166
A.3 Protected Steel Beam Temperature
The protected beam temperature calculation was also taken from Buchanan [3] and
is given below.
∆~ = -��zb5bu~J~
u~J~�u~J~ + �-� �⁄ � 5bubJb �⁄ � � − ~�∆" (A.6)
where zb is the thermal conductivity of the insulation (0.12W/m K)
5b is the thickness of the insulation (m)
ub is the density of the insulation (550kg/m3)
Jb is the specific heat of the insulation (1200J/kg K)
The material properties of the insulation were based on high density perlite, as
given by Buchanan. The thickness of the insulation was solved for using Eq. (A.6),
applying the standard temperature-time curve and limiting the steel temperature to
below 550°C for 60 and 120 minutes. This method should ensure a similar level of
performance for any insulating material used to achieve these fire ratings.
References
1 Incropera, F., DeWitt, D., Bergman, T., and Lavine, A., Fundamentals of Heat and
Mass Transfer, John Wiley & Sons, 2007.
2 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on
structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.
3 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.